First solve the system for x and y.

-3y+8x=18
y=6x-6

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 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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The expression for the function f(x) in standard form if the function f(x) is divided by x-2 is f(x) = 3x³ + 2x² - 20x + 17.

The function that when divided by 2x + 1, the quotient is x² - 8x + 8 and the remainder is 5 is determined as follows:

f(x) = (2x + 1)(x² - 8x + 8) + 5

Simplifying the above gives the following:

f(x) = 2x³ - 16x² + 16x + x² - 8x + 8 + 5

f(x) = 3x³ - 15x² + 8x + 13

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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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We can conclude that the division property of equality was done between step 4 and step 5.

What is linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

The Division Property of Equality states that when both sides of an equation are divided by the same nonzero number, both sides remain equal.

That is, if a, b, and c are real numbers such that a = b and c ≠0, then  

a/c = b/c

At step 4: The equation was -6x = 57

To move to step 5, Paula had to divide both sides by the co-efficient of x (-6) in order to get the value of x. See below

-6x = 57

---- Divide both sides by -6 (Step 4)

-6x / -6  = 57 / -6

---- (Intermediary between step 4 and 5)

x = -9.5

----- Step 5

Hence, we can conclude that the division property of equality was done between step 4 and step 5

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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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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:

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: 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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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

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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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.

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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Answer:

3 1/10 as a fraction

Step-by-step explanation:

3.3 as a fraction is 3 3/10. The first 3 is a whole number because it is to the left of the decimal point, and it represents 3 ''ones''. However, the second 3 to the right of the decimal point represents a decimal amount. Because this 3 is in the tenths place, we say it as ''3 tenths.

33 is repeating

    When converting a percent in fraction form, you must know its place value of each number, and you can easily transform it to fraction.

3.3% - the place value is ones. It is a whole number and called as three.

3.3% - the place value is tenths. It is called as three-tenths.

When you convert a percent to decimal, you must divide it by 100.

3.3 ÷ 100

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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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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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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Answer:

(A+7)^4

Step-by-step explanation:

Take the original data and divide it by the standard deviation to determine the z-scores. X is a symbol for the relevant data point. For the population from which you selected your sample, mu and sigma stand in for the mean and standard deviation.

In terms of standard deviations above or below the mean, a data point's z-score quantifies this exact distance.

A z-score is calculated using the following formula:

data point = mean standard deviation

Data point means with standard deviation equal to z

The same equation is given below in symbol form:

z=  x−μ / σ

Some significant z-score details are as follows:

An elevated z-score indicates that the data point is.

When a data point has a negative z-score, it is below average.

The data point is considered to be roughly average if the z-score is near to 0.00.

If a data point's z-score is higher or lower than 3 33 or 3 3minus, the data point is deemed uncommon.

At Almond, the average score on a history midterm is

= 85 = 85mu, which is equivalent to 85 with a standard deviation of

= 2 = 2 = 2 = 2 = 2 = 2 = 2 = 2

On the test, Michael received a score of 86.866.668.

Calculate Michael's exam grade in Z-score form.

His Grade = Mean Grade Standard Deviation

= 86 − 85 / 2

= 1 /2 = 0.5 z z z

= standard deviation of his grade and mean grade.

= 2 / 86−85

= 2 / 1 =0.5.

The z-score for Michael is 0.5, 0.50, and 5. He received a grade that was half a standard deviation higher than the mean.

​

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Answer:

5.80

Step-by-step explanation:

just to make the answer

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 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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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)

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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Answer:

148545

Step-by-step explanation:

it's easy enough

Answer: 3 - 2x

Step-by-step explanation:

Product = Multiplication

Product of 2 and x = 2*x

3 minus 2x

3-2x

Answer:

3−2×x or 3-(2xx)