at a school, 20 percent of the sixth-grade students said that jazz is their favorite kind of music. if 30 sixth-grade students prefer jazz music, how many sixth-grade students are at the school? explain your reasoning.

The slope of the given lines are representing that these lines are perpendicular.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, the pair of the equation are parallel, perpendicular, or neither y=-7/8x-1, 32x-28y=-36

Slope intercept form of both equations of a line

1)  y = -7/8x - 1

it is already in a slope intercept form

2) 32x - 28y = -36

-28y = -32x -36

y = 8/7x + 9/7

Since their slope is inverse and had a negative constant.

The slope of a perpendicular line from the slope of a given line is obtained by taking the negative reciprocal of the slope of the given line. If the slope of the given line is m1 and the slope of a perpendicular line is m2 then we have m2 = -1/m1.

Therefore, The slope of the given lines are representing that these lines are perpendicular.

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Answer: the decorator should order 2,844 square feet of carpet to replace the carpet in the east room of the White House.

Step-by-step explanation:

Area = Length x Width

Area = 79 feet x 36 feet

Area = 2,844 square feet

The values of  (f + g) (x),  (f - g) (x),  (fg) (x) and  (f /g) (x) for the functions are x/(x + 9) + x³, x/(x + 9) - x³, x³/(x³ + 9) and  1/ [x² (x + 9)] respectively

A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input

Since f(x) = x/(x + 9), g(x) = x³

(a) (f + g) (x) will be the addition of f(x) and g(x). That is:

(f + g) (x) = x/(x + 9) + x³  or  x³ +  x/(x + 9)

(b) (f - g) (x) will be the subtraction of f(x) and g(x). That is:

(f - g) (x) = x/(x + 9) - x³

(c) (fg)(x) substitute x = x³ into f(x). That is:

f(x)= x/(x + 9), g(x) = x³

(fg)(x)  = x³/(x³ + 9)

(d) (f/g)(x) will be the division of f(x) by g(x). That is:

(f/g)(x) = [x/(x + 9)] / x³ =  x/ [x³ (x + 9)] = 1/ [x² (x + 9)]

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The unit vector perpendicular to the plane of given vectors P =i−2j+ k and Q =2i + j − k is ( i + 3j + 5k )/√35

The vector that perpendicular to the plane is equal to the cross product of:

P ⨉ Q

Remember the properties of cross product of two vectors:

i ⨉ i = j ⨉ j = k⨉ k = 0

i ⨉ j = k

j ⨉ i = - k

j ⨉ k = i

k⨉ i = j

i⨉ k = -j

Hence,

P ⨉ Q = (i−2j+ k) ⨉ (2i+j−k)

          = k + j +4k + 2i +2j - i

          = i + 3j + 5k

The magnitude of P ⨉ Q is:

|| P ⨉ Q || = √(1² + 3² + 5²)

               = √35

Therefore, the unit vector = ( i + 3j + 5k )/√35

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True. A data model is an abstract representation of the data structures used in a database.

It is typically used to represent the structure of the data and the relationships between different elements of the data. Data models are used to define the structure of the data in a database, as well as the relationships between different elements of the data. A data model is a combination of entities, attributes, relationships, and constraints. It is used to describe the data that is stored in a database and how the data can be accessed and manipulated. The data model also defines the relationships between the different elements of the data, such as which element of the data is related to which other element. The data model also defines the constraints that must be met in order to ensure the integrity of the data. A data model is also used to define the data types that are used in the database and the operations that can be performed on the data. For example, a data model may define data types such as integers, strings, and dates, as well as operations such as arithmetic, comparison, and sorting. A data model also defines rules for the structure and organization of the data, such as which fields must be present in a record, the order in which records must be stored, and the types of relationships that can exist between records.

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The coordinates of the hooks in three-dimensional space are found and the mid-point of the string is recognised as (4.5, 6, 7.75).

What is meant by three-dimensional space?

A three-dimensional space in geometry is a mathematical structure where a point's location depends on three different values.

For this question, we are considering the east of origin as the positive x-axis, the above origin as the positive z-axis and the north of the origin as the positive y-axis.

a)  For the first hook there is no y-axis, it is hung in the xz plane.

So the coordinates are (4,0,7.5)

b) The second hook coordinates are given as (5, 12,8)

c) The point on the string which joins the hook, which is halfway between the hooks can be found using the mid-point formula.

x= (x1 + x2)/2 = (4+5)/2 = 4.5

y = (y1 + y2) /2 = (0+12) / 2 = 6

z = (z1+z2) / 2 = (7.5 + 8) /2 = 7.75

Therefore the mid-point of the string is (4.5, 6, 7.75).

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The slope of the given graph is 3/8 .

What is Graph ?

Graph can be defined as the visual representation in which we can represent the data.

Given in the graph,

We are given two points: (4, 5) and ( -4, 2 ). Slope is calculated as the change in y over the change in x, or rise over run.

The change in y is the difference of the two y coordinates (it doesn't matter the order): 5- (2) = 3

The change in x is the difference of the two x coordinates (this order depends on the order that you subtracted the y coordinates; they must be the same order): 4 - (-4) = 4+4 = 8.

So, the slope is 3/8

Therefore, The slope of the given graph is 3/8 .

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The picture shows James holding the clinometer 5.5 feet off the ground while pointing it up to the sun at an angle of 35 degrees. The equation to model this scenario is y = 5.5sin(35). To solve for y without using a calculator, we can use the inverse trigonometric function arcsin, so y = 5.5 arcsin(35). The answer is y = 4.51 feet.

y = 5.5sin(35)

y = 4.816

arcsin(4.816) = 35

4.816 = 5.5sin(35)

y = 5.5 arcsin(35)

y = 4.51 feet

The picture shows James holding the clinometer 5.5 feet off the ground while pointing it up to the sun at an angle of 35 degrees. The equation to model this scenario is y = 5.5sin(35), which is the length of the shadow. To solve for y without using a calculator, we can use the inverse trigonometric function arcsin, so y = 5.5 arcsin(35). We can then use the Pythagorean Theorem to solve for y: 4.816 = 5.5sin(35), so y = 5.5 arcsin(35). The answer is y = 4.51 feet, so the length of the shadow is 4.51 feet. This demonstrates how trigonometry can be used to calculate the length of shadows, with the help of a clinometer.

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The explicit equation and domain for an arithmetic sequence is a_{n}=9+(n-1)-8, the correct option is C

An arithmetic sequence is sequence of integers with its adjacent terms differing with one common difference.

If the initial term of a sequence is 'a' and the common difference is of 'd', then we have the arithmetic sequence as:

a, a + d, a +  2d, ... , a + (n+1)d, ...

Its nth term is

T_n = a + (n-1)d

(for all positive integer values of n)

And thus, the common difference is

T_{n+1} - T_n

for all positive integer values of n

Given;

A first term of 9 and a second term of 1

a=9

D=1-9=-8

We know that the explicit equation of an AP is

a_{n}=a_{1}+(n-1)d

So, substituting the values

a_{n}=9+(n-1)-8

Therefore, the arithmetic sequence will be a_{n}=9+(n-1)-8.

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Answer: 2343.8 meters

Step-by-step explanation: If 3.8 meters is walked in 1/2 hours then another 4680 meters per hour is ran for a half hour is 2340 meters add those 2 together

The required value of d for the given function is given as d = 2.

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol

Here,
F(s) = 5s²+ 4s +4
F'(s) = 10s + 4

F'(1) = f(d) - f(0)/ d
10(1) + 4 = 5d² + 4d / d
14 = 5d +4
d = 2

Thus, the required value of d is given as d = 2.

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Consequently, the plant will exhibit a tall phenotype as a result of the T allele's presence. In a heterozygous tall pea plant, the tall trait will therefore be visible.

Punnet square analysis indicates that the progeny of two heterozygous pea plants (Yy) will be 75% (3/4) dominant and 25% (1/4) recessive. In the event that 1000 individuals are created, 750 will therefore be dominating.

Tt will be the genotype of a tall heterozygous plant. It will actually prevail over the recessive t allele because T is primarily the dominant allele. Consequently, the plant will exhibit a tall phenotype as a result of the T allele's presence. In a heterozygous tall pea plant, the tall trait will therefore be visible.

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Answer:

There are 10,000 four-digit decimal numbers that have an estimated value of 10 when rounded off to the nearest tenths place. This is because each decimal number from 0.0001 to 0.9999 will have an estimated value of 10 when rounded off to the nearest tenths place.

Answer:

the probability of randomly selecting the chair and the vice chair is 10%.

Step-by-step explanation:

There are a total of 5 members on the health services committee, and 2 of them will be chosen to serve as the chair and vice chair, respectively.

The probability of randomly selecting the chair out of the 5 members is 2/5, or 40%.

Once the chair is selected, there are 4 members remaining, and only one of them can serve as the vice chair. Therefore, the probability of randomly selecting the vice chair out of the remaining 4 members is 1/4, or 25%.

To find the probability of randomly selecting the chair and the vice chair, we need to multiply the individual probabilities of selecting each position, which is (2/5) * (1/4) = 2/20 = 1/10 = 10%.

So, the probability of randomly selecting the chair and the vice chair is 10%.

Answer:

5.80

Step-by-step explanation:

just to make the answer

Answer:

148545

Step-by-step explanation:

it's easy enough

La tarjeta de crédito tiene una tasa efectiva de interés anual de 21,375 %.

En este problema tenemos que Merle obtiene una tarjeta de crédito bajo la siguientes condiciones: 0 % E.A. para los primeros 60 días, 23,19 % E.A. para los 365 restantes.

Debemos determinar la tasa de interés efectiva anual equivalente, esto es posiblemente mediante una aplicación consecutiva del concepto de interés, descrito abajo:

I = (1 + r / 36500)ⁿ

Donde:

La situación es descrita por la siguiente expresión matemática:

1 + R / 100 = (1 + 0 / 36500)⁶⁰ + (1 + 23,19 / 36500)³⁰⁵

Donde R es la tasa efectiva de interés anual.

Finalmente, despejamos la variable correspondiente:

R = 21,375

La tasa efectiva de interés anual a sufragar por Merle por el uso de tarjeta de crédito es 21,375 %.

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The area in square feet of the part of the backyard in which Shayne is allowed to dig is option D: 272 ft².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The length of the rectangle ADEH is 17 ft.

The breadth of the rectangle ADEH is 22 ft.

The length of the rectangle ABGH is 17 ft.

The breadth of the rectangle ABGH is -

GH = (EH - GE)

GH = [EH - (GF + EF)]

GH = [22 - (6 + 14)]

GH = [22 - 20]

GH = 2 ft

The formula for the area of a rectangle is -

Area = Length × Breadth

The area of part where Shayne is allowed to dig is -

Area = [Area of ABGH + Area of CDEF]

Area = [(17 × 2) + (17 × 14)]

Area = [34 + 238]

Area = 272 ft²

Therefore, the value for area is obtained as 272 ft².

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The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.

The upper bound of Valletta = Upper bound of Leeds - Copenhagen +23

upper bound of Valletta  = 16.8 -12+23

upper bound of Valletta = 27.8 °C

Lower bound of Valletta = 0.1 -12+23

Lower bound of Valletta = 10.9 °C

Hence, The lower and upper bounds of the temperature at noon in Valletta are 10.9° C and 27.8° C.

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In order to factor your quadratic polynomials, the box method, as its name suggests, uses a box. You can divide your quadratic into its factors by using the box, which is essentially a square divided into four equal parts.

Employing the Box Method

For our first quadratic, 6x2 - x - 12, let's utilize the box approach to solve it.

The first step is to create a two by two grid, as shown here:

using a box

Following that, we place the first term in the upper left box and the last term in the lower right box.

The Complete Question.

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The probability that the first two people to leave are science teachers is; 2/15

The parameters about the subject teachers are;

Number of maths teachers = 5

Number of Science Teachers = 6

Number of Social Studies Teachers = 5

Total number of teachers = 5 + 6 + 5

Total teachers = 16

Thus;

Probability that first to leave is a science teacher = 6/15

Probability that after the first leaves, the second to leave will be a science teacher = 5/15

Thus;

P(first two to leave are science teachers) = (6/15) * (5/15)

= 2/15

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To solve for the volume of the rotated region we will use the integration and its formula is V=π∫ba(r21−r22)h where r1 and r2 are the radii of the washer and h is the height. Note that the limits a and b is determined by finding the volume of the solid .

Using the washer method, the volume of the solid is

V=π∫ba[(x14)2−(x4)2]dx

Find the limits, equate the two equations in terms of x

4√x=x4

Raising both sides to fourth power,

x=x8x8−x=0

Factor out x

x(x7−1)=0

x=0,1

Thus, the limits is from x =

V=π∫10[(x^1/4)^2−(x4)^2]dx

Integrate this equation with in limits 0 to 1

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so hmm £36000 will be split, hmmm let's call the ratios "a,b and c", so the amount will be split in ratios of a : b : c, which means we'll be dividing the 36000 bucks by (a + b + c) and distribute accordingly, let's do that, hmm let's convert also all those mixed fractions to improper fractions.

[tex]\stackrel{mixed}{2\frac{3}{4}}\implies \cfrac{2\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{11}{4}} ~\hfill \stackrel{mixed}{1\frac{1}{2}} \implies \cfrac{1\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{3}{2}} \\\\\\ \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} ~\hfill \boxed{\cfrac{11}{4}+\cfrac{3}{2}+\cfrac{9}{4}\implies \cfrac{13}{2}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\cfrac{36000}{~~ \frac{13 }{2 } ~~}\implies 36000\cdot \cfrac{2}{13}\implies \cfrac{72000}{13} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{Alex}{\cfrac{11}{4}\cdot \cfrac{72000}{13}}~~ : ~~\stackrel{Bill}{\cfrac{3}{2}\cdot \cfrac{72000}{13}}~~ : ~~\stackrel{Claire}{\cfrac{9}{4}\cdot \cfrac{72000}{13}}\implies \stackrel{Alex}{\cfrac{198000}{13}}~~ : ~~\stackrel{Bill}{\cfrac{108000}{13}}~ : ~\stackrel{Claire}{\cfrac{162000}{13}} \\\\\\ ~\hfill \stackrel{Alex}{15230\frac{10}{13}}~~ : ~~\stackrel{Bill}{8307\frac{9}{13}}~ : ~\stackrel{Claire}{12461\frac{7}{13}}~\hfill[/tex]

Answer:

4

--

3

Step-by-step explanation:

Rate of Change via a table should be

f(x2)-f(x1)

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

x2 - x1

In this problem they indicated X2 is 36 and X1 is 18

At 36, F(X) is 61 and for 18, it's 37

Now to plug in...

61 - 37

----------

36 - 18

That boils down to

24

----

18

If we want to simplify it;

4

--. or. 1.333

3

The simplified expressions that we have are;

a) 2∛16 - 12

b) (-375)^1/3x^8/3y^8/3

The term simplifications means that we have to write the expression is the easiest way that it can be written. In this case we have two expressions. We can be able to simplify them as we work through the steps that have been written below;

8) -2∛81 + 2∛16 - 2∛81

-4∛81 + 2∛16

-4(3) + 2∛16

2∛16 - 12

10) ∛-375x^8y^8

This simplifies to;

(-375)^1/3x^8/3y^8/3

This is the way that we can be able to simplify the expressions here.

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Reason:

The 6x-x on the right hand side simplifies to 5x

This means the right hand side turns into 5x-11, which is an identical copy of the 5x-11 on the left side.

The equation 5x-11 = 5x-11 has infinitely many solutions because we can replace x with any real number to end up with a true statement.

Answer:

Step-by-step explanation:

1/3 + 2i is a complex number, with the real part equal to 1/3 and the imaginary part equal to 2i. It can be represented in a Cartesian coordinate system as a point (1/3, 2)

The expression in the standard form  is 37.008

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

3 x 10 + 6 x1 + 1 + 8 x 1/1,000

Evaluate the products

This gives

30 + 6 + 1 + 8/1,000

Evaluate the quotients

30 + 6 + 1 + 0.008

Evaluate the sum

37.008

Hence, the number in standard form is 37.008

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