(Marks: 9) If your current age is x years, and 9 years later your age will be 4 less than double of your current age, then an equation representing the statement is:

X + 9 = 2x - 4

X-9 = 2x - 4

X + 9 = 2x + 4

X-9 = 2x + 4​

We can identify a correct system of equations after draw the graph of the system. The point of intersection indicates the correct solution of the system.

Two or more equations which have the same variables, and we can use these all together. The equations are called a set of equations. We get the solution from the system while plotting in the XY coordinate system.

Such as we have two or more linear equations, and we solve each equation and draw a graph for each. We will notice a point of intersection of the straight lines and that refers the solution of the system of equation.

There are many sets or system of equation. Some systems have infinity many solutions and graph of the equations never intersect each other. In the next, there are system of equations such as a set of linear function from where we get a point of intersection after plotting the graphs together. The line of intersection is the correct solution of the system.

On the other hand, there are some sets which have no solution, and they are called inconsistent.

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On integrating the function f(x), we get - (x³/45) + (3x²) - (2x³) + C.

        [tex]$\int_a^b \! f(x) \, \mathrm{d}x.[/tex]

Given is the function, as follows -

f(x) = (x²/15 + 6x - 9x²/{3/2})

The given function is -

f(x) = (x²/15 + 6x - 9x²/{3/2})

∫f(x) = ∫(x²/15 + 6x - 9x²/{3/2}) dx

∫f(x) = ∫(x²/15)dx + ∫(6x)dx - ∫(6x²)dx

∫f(x) = (1/15)(x³/3) + C₁ + (6)(x²/2) + C₂ - (6)(x³/3) + C₃

∫f(x) = (x³/45) + (3x²) - (2x³) + {C₁ + C₂ + C₃}

∫f(x) = x³/45) + (3x²) - (2x³) + C                  (C = C₁ + C₂ + C₃)

Therefore, on integrating the function f(x), we get (x³/45) + (3x²) - (2x³) + C.

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6.25% is the the sales tax.

Percentage, a relative value indicating hundredth parts of any quantity.

Given that a store manager notes that gold rings that retail for $688 end up

costing customers $731 once the sales tax is added.

We need to find the sales tax percentage.

The percentage we can calculate by subtracting original amount minus new amount by original amount and multiplied with 100.

731-688/688

0.0625

Multiply 0.0625 with 100 as it is a hundredth part.

0.0625×100

6.25%

Hence, the sales tax percentage is 6.25%.

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The numerical expression is -4(5+(-2)) by solving we get -12 is the number with a negative term.

Given that,

The expression is -4(5+(-2))

We have to find what is the solution for the given numerical expression.

We know that,

Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Take the numerical expression

-4(5+(-2))

Adding 5+(-2)

Multiply + - we get -

So,

5-2=3

-4(5-2)=-4(3)

Multiply 4 to 3

-4(3)=-12

Therefore, The numerical expression is -4(5+(-2)) by solving we get -12 is the number with a negative term.

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-5 + 13x = 60

13x = 65

x = 5

CHECKING:

-5 + 13(5) = 60

-5 + 65 = 60

60 = 60

Step-by-step explanation:

Part a: The margin of error and the interval estimate is E = 0.027 and 0.6120 < p < 0.666 respectively.

Part b:  The margin of error and the interval estimate is E = 0.027 and 0.3900 < p < 0.4440 respectively.

Considering the first query;

Since the confidence level for the question is 95%, the level of importance is;

α = (100 - 95)%

α = 0.05

Typically, the crucial value of comes out from normal distribution table of α/2 is;

Z(α/2) = 1.96

Typically, this margin of error is denoted mathematically as follows:

E = Z(α/2)*√P₁(1 - P₁)/n

E = 1.96*√0.639(1 - 0.639)/1200

E = 0.027

Mathematically, a 95% Interval estimate is typically written as;

P₁ - E < p < P₁ +E

0.639 - 0.027 < p < 0.639 + 0.027

0.6120 < p < 0.666

Thus, the margin of error and the interval estimate is E = 0.027 and 0.6120 < p < 0.666 respectively.

Part (b)

Since the confidence level for the question is 95%, the level of importance is;

α = (100 - 95)%

α = 0.05

Typically, the crucial value of comes from the normal distribution table and is;

Z(α/2) = 1.96

Typically, the margin of error is denoted mathematically as follows:

E = Z(α/2)*√p₂(1 - p₂)/n

E = 1.96*√0.417(1 - 0.417)/1200

E = 0.027

Mathematically, a 95% Interval estimate is typically written as;

P₁ - E < p < P₁ +E

0.417 - 0.027 < p < 0.417 + 0.027

0.3900 < p < 0.4440

Thus, the margin of error and the interval estimate is E = 0.027 and 0.3900 < p < 0.4440 respectively.

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The complete question is-

Fewer young people are driving. In 1995, 63.9% of people under years 20 old who were eligible had a driver's license. Bloomberg reported that percentage had dropped to 41.7% in 2016. Suppose these results are based on a random sample 1,200 of people under 20 years old who were eligible to have a driver's license in 1995 and again in 2016.

a. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 1995?

Margin of error(to four decimal places)

Interval estimate (to four decimal places)

b. At 95% confidence, what is the margin of error and the interval estimate of the number of eligible people under 20 years old who had a driver's license in 2016?

Answer:

The answer is ab32

Step-by-step explanation:

ab x 8 x 4 = ab32

Answer: a^4b^32

Step-by-step explanation: (ab^8)^4 = (ab^8)(ab^8)(ab^8)(ab^8) = a^4b^32

Check the picture below.

Answer:

14.1

Step-by-step explanation:

You add all of your numbers up, and then you divide by how many numbers you have.

We are given that the probability of selecting a yellow card is 3 times the probability of selecting a blue card, so we can write the following equation:

yellow = 3 * blue

We also know that the sum of the probabilities of selecting a red, yellow, or blue card must be equal to 1, so we can write the following equation:

red + yellow + blue = 1

Substituting the expression for yellow from the first equation into the second equation, we get:

red + 3 * blue + blue = 1

Combining like terms, we get:

red + 4 * blue = 1

We are given that the probability of selecting a red card is 1/9, so we can substitute this value into the equation:

1/9 + 4 * blue = 1

Solving for blue, we get:

blue = (1 - 1/9) / 4

blue = (8/9) / 4

blue = 2/9

Therefore, the probability of selecting a blue card on the first try is 2/9.

Answer:

i believe its 5+n ≤ -7

Step-by-step explanation:

the sum of 5 and a number(n) would be 5+n, and no more woukd be the  ≤  sign, which would lead to -7

An equation of line having slope 1/4 and passes through the point (-4,-3) is y = 1/4x - 2

We know that the slope-point form of line is:

(y - y1) = m(x - x1)

Here, we need to find an equation of line having slope 1/4 and passes pae through the point (-4,-3)

let (x1, y1) = (-4, -3)

and m = 1/4

substitute values in above formula,

(y - (-3)) = 1/4 (x +4)

y + 3 = 1/4 (x+4)

y = 1/4x -2

which is slope-intercept form of line (y = mx + b)

Therefore, equation of line is y = 1/4x - 2

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Answer: Zeli shan tel

Step-by-step explanation:

The first quartile of miles driven is 218 miles.

Quartiles are three values ​​that divide the sorted data into four parts, each of which has the same observation value.

The four quarters that divide the dataset into quartiles are:

Let's arrange the data in an order:

211,212,218,223,231,233,245,261,278,299

Since the data has 10 observation, for which the median will be simply the average of two middle terms i.e.5th and 6th term dividing the data in two halves.

Median: 232

First half: 211,212,218,223,231

Second half: 233,245,261,278,299

As, quartiles are the medians of each half,

First quartile: 218

Third quartile: 261

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The domain of the function y = 2x + 5 is [-4, 1), and the range of the function is  [5, 7). The graph is also attached below.

A collection of objects is arranged in a graph, where some object pairings are conceptually "linked." Each pair of connected vertices is referred to as an edge, and the objects are represented by mathematical abstractions known as vertices.

Given:

As you can see from the graph, the coordinates of the line are (0, 5) and (1,7),

Calculate the equation of the line as shown below,

y - 5 = (7 - 5) / (1 -0) (x-0)

y - 5 = 2 (x +0)

y = 2x + 5

The domain of the above equation can be determined from the graph,

Domain = [-4, 1)

Range = [5, 7)

The graph is also attached below.

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The centroid of the region in the first quadrant bounded by the given curves is (81/170, 81/170).

In the given question, we have to find the centroid of the region in the first quadrant bounded by the given curves.

The given curves are:

y = x^8, x = y^8

We can write the curves as

y = x^8...........................(1)

y = x^{1/8}.......................(2)

Now putting the value of y from equation 1 in equation 2, we get

x^8 = x^{1/8}

Now simplifying,

x^{64} = x

x^{64}-x = 0

x(x^{63} - 1) = 0

After equating equal to zero,

x = 0, x = 1

My = [tex]\int_{a\rightarrow b}x[f(x)-g(x)]dx[/tex]

My = [tex]\int_{0}^{1}x[x^{1/8} - x^{8}]dx[/tex]

My = [tex]\int_{0}^{1}[x^{9/8} - x^{9}]dx[/tex]

My = [tex][(8/17)x^{17/8} - (1/10)x^{10}]_{0}^{1}[/tex]

My = (8/17)-(1/10)

My = 63/170

Mx = 1/2[tex]\int_{a\rightarrow b}[(f(x))^2-(g(x))^2]dx[/tex]

Mx = 1/2[tex]\int^{1}_{0}[x^{1/4} - x^{16}]dx[/tex]

Mx = 1/2 [tex][(4/5)x^{5/4} - (1/17)x^{17}]^{1}_{0}[/tex]

Mx = (1/2)[(4/5)- (1/17)]

Mx = 63/170

M = [tex]\int_{a\rightarrow b}[f(x)-g(x)]dx[/tex]

M = [tex]\int^{1}_{0}[x^{1/8} - x^{8}] dx[/tex]

M = [tex][(8/9)x^{9/8} - (1/9)x^{9}]^{1}_{0}[/tex]

M = [(8/9) - (1/9)]

M =7/9

Center of mass(x',y') = (My/M, Mx/M)

Center of mass(x',y') = ((63/170)/(7/9), (63/170)/(7/9))

Center of mass(x',y') = (81/170, 81/170)

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Answer:

7.4 mins

Step-by-step explanation:

135 -----> 1 min

1000 ----> x

1000/135 mins = x

= 7.4 mins

Answer:

To determine how long it will take to fill 1000 containers at a rate of 135 containers per minute, you can use the formula: time = number of containers / filling rate. In this case, the filling rate is 135 containers per minute, and the number of containers you want to fill is 1000. Plugging these values into the formula, we get: time = 1000 / 135 = 7.41 minutes.

answer:

if because x does not have two y

Step-by-step explanation:

I hope it works

At any point p(x, y), the tangent line to a particular curve has an x-intercept of 3 4 x. The point is also traversed by this curve (1, 16). The equation of the curve is y - 16 = (3/4)(x - 1)^2

To find the equation of the curve, we first need to find the equation of the tangent line at point P(x, y).

Since the x-intercept is 3/4x, the equation of the tangent line is

y - y_p = (3/4)(x - x_p).

We substitute the given point (1, 16) in the equation to find the value of y_p and x_p which are 16 and 1 respectively.

y - 16

= (3/4)(x - 1).

This equation is the equation of the curve.

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Answer:

25.12 in.

Step-by-step explanation:

C = 2πd

C = 2 × 3.14 × 4 in.

C = 25.12 in.

The sum of the first 20 terms of the geometric sequence is 20.25.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16, 32 is a geometric sequence.

We have,

27, -9, 3, -1,.....

a = 27

Common ratio:

= -9/27 = -1/3

= 3/-9 = -1/3

The sum of the geometric sequence.

S(n) = a (1 - [tex]r^n[/tex]) / (1 - r)

Now,

a = 27,

r = -1/3

S(20):

= 27 (1 - [tex](-1/3)^{20}[/tex]) / (1 + 1/3)

= 27 (1 + 1/[tex]3^{20}[/tex]) / (4/3)

[ (1 + 1/[tex]3^{20}[/tex]) = 1 ]

= 27 x 3/4 x 1

= 20.25

Thus,

The sum of the geometric sequence is 20.25.

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Answer: It should be 3rd onem 3/4n=5/8

Step-by-step explanation: if not my bad-

The equation of the line is y = x. Then the rule of reflection is (x, y) ⇒ (y, x).

It is the image of the point which is located in the opposite direction of a given point.

The rule of the refection is given will be

Firstly, the rule for reflecting a point about the line y = x is;

While reflecting on the line y = x, we get the reflected points by swapping the coordinates.

The equation of the line that passes through (0, 0) and (1, 1) is given as,

y - 0 = [(1 - 0) / (1 - 0)](x - 0)

y = x

The equation of the line is y = x. Then the rule of reflection is given as,

(x, y) ⇒ (y, x)

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The equation of the transformed function is g(x) = -x² - 2

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

f(x) = x² -- parent root function

When the graph is examined (see attachment), we have the transformation to be

g(x) = reflect f(x) across the x-axis and a downward shift of 2 units.

Mathematically, this can be represented as

g(x) = -f(x) - 2

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

g(x) = -x² - 2

Hence, the transformed function is g(x) = -x² - 2

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Answer:

the anwser is b

Step-by-step explanation:

Answer:

To prove that 16^5+16^4 is divisible by 17 using factoring, first rewrite the expression 16^5+16^4 using the distributive law as 16^4*(16+1). Then, note that 16+1 is divisible by 17. Since 16^4 is also divisible by 17, the expression 16^4*(16+1) is also divisible by 17. Therefore, 16^5+16^4 is divisible by 17.

The answer is 11(a - b), To solve this expression, we need to perform the subtraction operation on the terms inside the parentheses. First, we subtract the term "a + 6b" from "12a - 5b". This gives us 11a - 11b. Then, we can simplify this expression by combining the like terms 11a and -11b to get 11a - 11b = 11(a - b). This is the final answer.

This equation is incorrect because it is missing a division sign between 1.7 and 0.65p. The correct equation should be t = (1.7 / 0.65p) * 0.10

First, we need to isolate the variable 't' in the equation. To do this, we need to divide both sides of the equation by 0.10. This will give us 0.65p/0.10 = 1.70/0.10, which simplifies to t = (1.7 / 0.65p) * 0.10. This is the correct equation that we need to solve for 't'.

t = (1.7 / 0.65p) * 0.10

t = (1.7 / (0.65 * p)) * 0.10

t = (17 / (6.5 * p)) * 0.1

t = (17 * 0.1) / (6.5 * p)

t = (1.7) / (6.5 * p)

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Total no of racks in the store is 30 and grocery item is maximum.

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

Divide the amount by the total value to get the percentage, then multiply the resulting number by 100.

Racks of confectionery items = 10

Racks of bread items = 5

Racks of grocery items = 15

The total no of racks in the departmental store is 30

Using the percentage formula we will calculate the percentage of each item

percentage of confectionery items rack =no. of confectionery racks/total no. of racks  x100

=10/30x100=33.33%

percentage of bread items rack = no. of bread racks/total no. of racks x 100

= 5/30x 100=16.66%

percentage of grocery items rack = no. of grocery racks/total no. of racks x 100

= 15/30 x 100 = 50%

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