in a recent​ survey, ​% of the community favored building a police substation in their neighborhood. if 14 citizens are​ chosen, find the probability that exactly of them favor the building of the police substation. round the answer to the nearest thousandth.

The vertex f(x) = x² - 8x +7 is (4,-9)

A quadratic equation is a second-order polynomial equation with a single variable, such as x = ax2 + bx + c = 0, where a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated. Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.

Given Data

Establishing the axis of symmetry is the first step that you should take (the x co-ordinate of the vertex). You must factor the equation in order to do this. You need to find two values that sum up to -8 and multiply to +7 in order to factor this easy trinomial. This pair of numbers, -1 and -7, means:

-7 x -1 = +7 \s-7 + -1 = -8

Now, you take these two components and mark each one with an x in brackets as follows:

f(x) = (x -1)(x-7)

Set each bracket to zero now, and then solve. Get x = 7 and x = 1, respectively. Add the zeros together and divide by 2 to find the axis of symmetry:

[tex]\frac{7+1}{2}[/tex]

= 4

Consequently, x=4 is the equation for the axis of symmetry.

You may now insert the axis of symmetry into the equation (either the factored version or the original; in this case, factored would be the simplest) to obtain the best value (y co-ordinate of the vertex):

f(4) = (4-1)(4-7)

f(4) = (3)(-3)

f(4) = -9

Therefore, -9 is the ideal value.

Together, it makes the vertex (4, -9)!

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If Mr. Jamison bought 8 dozen sketch pencils, 6dozen colored pencils and 3 dozen art gum, with a sales tax of 8 percent, considering each dozen of sketch pencils costed $x, colored pencils costed $y and art gums costed $z, the total bill approximately would be

$[(8x + 6y + 3z) + 0.08(8x + 6y + 3z)].

As per the question statement, Mr. Jamison bought 8 dozen sketch pencils, 6dozen colored pencils and 3 dozen art gum, with a sales tax of 8 Percent, and since no information is provided about the price of the sketch pencils, colored pencils or art gums, let us consider that each dozen of sketch pencils costed $x, colored pencils costed $y and art gums costed $z.

We are required to calculate the total approximate bill, Mr. Jamison would have to pay for the items he picked up.

To solve this question, first we will have to calculate the total price of the items he picked, without any taxes, i.e.,

$[(8 * x) + (6 * y) + (3 * z)] = $(8x + 6y + 3z).

Now an 8% sales tax on the price of the items bought will be

8% of $[(8x + 6y + 3z), i.e.,

[(8/100) * (8x + 6y + 3z)]

= $[0.08(8x + 6y + 3z)]

Therefore, total bill = (Total item costs + tax)

                                = $(8x + 6y + 3z) + $[0.08(8x + 6y + 3z)]

                                = $[(8x + 6y + 3z) + 0.08(8x + 6y + 3z)]

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Given the following expression:

Recall: In dividing fractions, you convert the equation into multiplication and multiply the dividend by the reciprocal of the divisor.

We get,

The same well-liked crackers are discounted at Value Grocery Mart and Market City are 5.25, 10.5,  15.75, and 21.

As the cost per pack is C=1.75b. C is the Cost in dollars.

3×1.75=5.25

6×1.75=10.5

9×1.75=15.75

12×1.75=21

An example of a chart is one that uses symbols to depict the data, such as bars in a bar chart, columns in a line chart, or slices in a pie chart.  A chart can convey various information by representing tabular numerical data, functions, or certain types of quality structures.

Users can change numerous rows and columns in a table at once using a tabular form and a single page.

A chart displays data that can be shown as a table, graph, or diagram. There are different ways to convey vast amounts of information in it.

Here, the table is.

Number of Boxes of Crackers ║   Grocery Mart  ║    Market City:

  3                                              ║       5                  ║  5.25

 6                                                ║     10                   ║ 10.5

 9                                                ║      15                   ║ 15.75

 12                                              ║      20                    ║ 21

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The most appropriate choice for percentage and fraction will be given by-

The process of conversion of fraction to percentage has been explained.

What is fraction and percentage?

Suppose there is a whole collection of objects and some parts of the objects are taken from the whole collection. Fraction represents those parts which are taken. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

If a number is taken as fraction of 100 then the fraction is known as percentage.

To convert a fraction into percentage, we have to simply multiply the fraction with 100.

For example.

Suppose we have a fraction [tex]\frac{1}{4}[/tex], we need to convert  [tex]\frac{1}{4}[/tex] to percentage.

So on multiplying [tex]\frac{1}{4}[/tex] by 100, we obtain = [tex]\frac{1}{4} \times 100[/tex] = 25%

So, [tex]\frac{1}{4}[/tex] is equivalent to 25%

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Answer:

800/920

400/460

40/46

20/23

Answer: Janessa would have 27 and Emily would have 19.

Answer:

[tex]x = 16[/tex]

Step-by-step explanation:

Because of the fact, the angle is ∠BCA = 10x - 10 and ∠ABC = 30 lies on a straight line and ∠BCA is obtuse while ∠ABC is acute, we can just set them equal to 180 to find the value of x.

So we will set up the equation:
   10x - 10 + 30 = 180

1. Combine Like Terms (eg. -10 and 30)
[tex]10x - 10 + 30 = 180[/tex]
= [tex]10 x + 20 = 180[/tex]

2. Subtract 20 on both sides
[tex]10x + 20 = 180[/tex]
       [tex]-20 -20[/tex]

= [tex]10x = 160[/tex]
3. Divide 10 into both sides
[tex]\frac{10x}{10} = \frac{160}{10}[/tex]

And we will get:
[tex]x = 16[/tex]

Check Your Work!
Now if we replace x in the equation for 16 like below we do in fact get 180:
[tex]10(16) - 10 + 30 = 180[/tex]
[tex]160 - 10 + 30 = 180[/tex]

[tex]150 + 30 = 180[/tex]

The given expression '5 × (2 + 4) = 6' can solve the problem (C).

So, 5 × (2 + 4) = 6:

(A) To solve the situation (A), the expression will be:

(B) To solve situation (B), the expression will be:

(C) To solve the situation (C), the expression will be:

Therefore, the given expression '5 × (2 + 4) = 6' can solve the problem (C).

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The correct question is given below;
Which problem could be solved with the expression

5 × (2 + 4) = 6?

Choose 1 answer:

A. Khai, the dog, ate 2 bones on Monday, 4 bones on Tuesday, and 6 bones on Wednesday. On Thursday, she ate 5 times more bones than the other days combined. How many bones did Khai eat on Thursday?

B. Hayden made 2 bracelets before school and 4 after school each day for 5 days. Then he split the bracelets into 6 equal groups. How many bracelets did Hayden have in each group?

C. Shadi is building a new back deck. He puts 2 nails and 4 screws in each board. He did this to 5 boards. How many total screws and nails did he use?

Answer: C. Hayden made 2 bracelets before school and 4 after

school each day for 5 days. Then he split the

bracelets into 6 equal groups. How many bracelets

did Hayden have in each group?

Step-by-step explanation:

For m =60 minutes The Fahrenheit temperature of a cup of coffee is approximately equals to 86°F.

What is an exponential function?

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable.

It is given that :

The Fahrenheit temperature of a cup of coffee cools down according

to the exponential function :

F(m) = 113 (¹/₂)^(m/20) + 72

where , m = number of minutes it has been cooling.

Now, for m = 60 minutes :

F(m) = 113 (¹/₂)^(m/20) + 72

F(60) = 113 (¹/₂)^(60/20) + 72

F(60) = 113 (¹/₂)³ + 72

F(m) = 113 /8 + 72

F(m) = 14.125+ 72

F(m) = 86.125°F

Therefore, For m =60 minutes The Fahrenheit temperature of a cup of coffee is approximately equals to 86°F.

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Using BODMAS

From the calculations above, the standard form is 1.87

Problem

Solution

For this case the surface area is given by:

And solving we got:

The answer is sum 5. Sum is a way to combine everything. The sum combines two or more numbers to produce a new total. In addition to "sum," other words that can be used in place of "sum" include "all together," "put together," "how many in all," and "total."

 Hence the Sum is 5.

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Answer:

x - 13

Step-by-step explanation:

To get this equation, we must look at the description.

13 less than x makes an equation of x - 13.

The answer is x - 13.

Hope this helps!

Btw, could I get a Brainliest? Thanks!

The least common denominator is  [tex]$&\frac{2}{3 b q}[/tex].

The smallest number that is precisely divisible by each denominator of a group of fractions is known as the lowest common denominator.

The lowest common multiple of the denominators of a group of fractions is known as the lowest common denominator, or LCD, in mathematics. It makes adding, taking away, and comparing fractions easier.

When two or more fractions are supplied, the least common denominator is the smallest number among all the common multiples of the denominators.

The smallest number that is precisely divisible by each denominator of a group of fractions is known as the lowest common denominator. It is occasionally referred to as the lowest common denominator.

a) [tex]$\frac{2 q}{3 b q^2}$$[/tex]

Apply exponent rule:

[tex]$\frac{x^a}{x^b}=\frac{1}{x^{b-a}}$[/tex]

substitute the values in the above equation, we get

[tex]$&\frac{q^1}{q^2}=\frac{1}{q^{2-1}} \\[/tex]

simplifying the above equation, we get

[tex]$&=\frac{2}{3 b q^{2-1}}[/tex]

Subtract the numbers,

[tex]$=\frac{2}{3 b q^1}$$[/tex]

Apply exponent rule:

[tex]$&q^1=q \\[/tex]

[tex]$&=\frac{2}{3 b q}[/tex]

b) [tex]$\frac{3 b^2}{7 b^4 q}$$[/tex]

Apply exponent rule, we get

[tex]$\quad \frac{x^a}{x^b}=\frac{1}{x^{b-a}}$[/tex]

substitute the values in the above equation, we get

[tex]$&\frac{b^2}{b^4}=\frac{1}{b^{4-2}} \\[/tex]

[tex]$&=\frac{3}{7 b^{4-2} q}[/tex]

Subtract the numbers:

[tex]$=\frac{3}{7 b^2 q}$$[/tex]

[tex]$\frac{4 q^2}{8 b^2 q^5}$$[/tex]

Factor the number:

[tex]$=\frac{4 q^2}{4 \cdot 2 b^2 q^5}$$[/tex]

Cancel the common factor,

[tex]$=\frac{q^2}{2 b^2 q^5}$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{q^2}{q^5}: \frac{1}{q^3}$[/tex]

[tex]$=\frac{1}{2 b^2 q^3}$$[/tex]

Therefore, the correct answer is option a) [tex]$&\frac{2}{3 b q}[/tex].

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The equation is y = [tex]\sqrt{x+5} + 5[/tex]. It is the graph of [tex]y = \sqrt{x}[/tex] translated 4 units right and 5 units up .

The slope-intercept form of a linear equation is y = mx + b. In the equation, x and y are the variables. The numbers m and b give the slope of the line (m) and the value of y when x is 0 (b). The value of y when x is 0 is called the y-intercept because (0,y) is the point at which the line crosses the y-axis.

The first method is by plotting all points on the graph and then drawing a line through the points.

The second is by using the y-intercept of the equation and slope of the equation.

Graph using the end point and a few selected points.

x       y

−

4      5

−

3      7

−

2     7.83

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The point slope from the line with slope -3/7 that passes through the point (5,8) is y-8 = -3/7 ( x-5).

Two crucial constants are present in a linear function: the slope, which is represented by the letter m, and the y-intercept, which is represented by the letter b. Y = m x + b is the slope-intercept equation's formula. The point-slope equation is a different manner that we can occasionally express the equation of a line. It reads as follows y-y₀ = m(x-x₀).

Given that :

Slope m = -3/7

passes through the point p ( 5, 8 )

Equation is  y-y₀ = m(x-x₀)

y-8=-3/7 ( x-5)

here the point slope is y-8=-3/7 ( x-5)

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The value of x in expression 4x² = 100 is, x =+5,-5

Blank 1 - division. Blank 2 - 100, Blank 3 - 25 , Blank 4- square

Blank 5- root, Blank 6- 5

A mathematical expression is made up of a statement, at least one arithmetic operation, and at least two integers or variables.

Mathematical expression components:

a) Constant: a fixed numerical value

b Variables: They don't accept any predetermined values. Values are assigned based on the criteria.

c)Terms: Constants, variables, or constants multiplied by variables are all acceptable terms (s).

d) Operators:The four operations of addition (+), subtraction (-), multiplication (-), and division (-) are referred to as operators because they are employed to combine the components in an equation.

Given:

4x² = 100

x² = 100 /4

x² = 25

√x² = √25

x = +5,-5

Blank 1 - division.

Blank 2 - 100

Blank 3 - 25

Blank 4- square

Blank 5- root

Blank 6- 5

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Step-by-step explanation:

the axis of symmetry for a regular parabola (opens up or down) is a line parallel to the y-axis (vertical) going through the vertex of the parabola.

the standard form of a parabola is

y = a(x - h)² + k

with (h, k) being the vertex.

so, we see for f(x) the vertex is (-4, 1).

the axis of symmetry uses the x coordinate of the vertex and is

x = -4

for h(x) we see in the graphic that the vertex is (1, -3).

so, the axis of symmetry is

x = 1

FYI - based on what we see : vertex is (1, -3), h(0) = -1 the function here would be

h(x) = 2(x - 1)² - 3

The main difference between end behavior of a quadratic and cubic function is as x approaches the negative infinity quadratic function goes to positive infinity and cubic function goes to negative infinity

What is the end behavior of the function?

The end behavior of the function means how function behaves when x approaches to ±∞

In case of an quadratic function when we substitute  ±∞ the values approaches to positive infinity And in case of the cubic function the value approaches to negative infinity

This is the difference

Hence end behavior of a quadratic  is as x approaches the negative infinity quadratic function goes to positive infinity and in cubic function goes to negative infinity

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The distance between the two points (-2, 4) and (3, 7) is found as 5.83.

For the given question;

The two coordinates are-

(x1, y1) = (-2, 4)

(x2, y2) = (3, 7)

The distance between two points are calculated as-

d = √(x1 - x2)² + (y1 - y2)²

Put the values;

d = √(-2 - 3)² + (7 - 4)²

d = √25 + 9

d = √34

d = 5.83

Thus, the distance between the two points (-2, 4) and (3, 7) is found as 5.83.

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The points (2, - 5) and (- 1, 1) lie on the equation of the line - 2 · x - y = 1.

According to Euclidean geometry, a line can be constructed from two distinct points on a plane. Then, we can find the equation of the line based on the coordinates of two points set on Cartesian plane, whose standard form is shown below:

a · x + b · y = 1

In this question we have the coordinates of two points: (2, -5), (- 1, 1). If we substitute in the equation of the line, then we find the following system of linear equations:

2 · a - 5 · b = 1

- a + b = 1

Then, we find the solution to the system by using numerical methods:

(a, b) = (- 2, - 1)

The equation of the line - 2 · x - y = 1 contains the points (2, - 5) and (- 1, 1).

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The answer as a decimal to the nearest hundredth is -3.45.

For the given question;

The expression is given as;

= -3.7 + 1/4

Now, the fraction 1/4 can be written in decimal as 0.25.

Put the value of 1/4.

=  -3.7 + 0.25

The subtraction of larger negative to smaller positive gives negative number.

= -3.45

Thus, the answer as a decimal to the nearest hundredth is -3.45.

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The 1st quarter for the data set is 46, 3rd quarter is 67 and the interquartile range is 21.

What is a quartile of a data set and how is it conceived?
A quartile is a set of values with three points that divides a data set into four equally sized portions. The values that divide a list of numerical data into three quarters are known as quartiles. The center of the three quadrants measures the point of distribution's center and displays data that are close to the center. Only half of the data set is represented by the lower part of the quarters, which is below the median, while the upper section represents the other half, which is above the median. The distribution or dispersion of the data set is shown overall by the quartiles.
When the data points are organized in ascending order, 25% of them are found in the lower quartile, often known as the first quartile (Q1). When presented in increasing order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).
Mathematically, First quartile (Q1) = [(n+1)/4] term
Third quartile (Q3) = [3(n+1)/4] term
The interquartile range is calculated as: Upper Quartile – Lower Quartile = Q3 - Q1

Arranging the given values in ascending order, we have the data set:
40, 42, 46, 47, 51, 55, 58, 67, 67, 68, 69
The total number of terms in the data set = n = 11
Using the formulae established in the literature, we have:
Now, first quartile = Q1 = [(11+1)/4] term = 3rd term = 46
Again, third quartile = Q3 = [3(11+1)/4] term = 9th term = 67
Therefore, interquartile range = Q3 - Q1 = 67 - 46 = 21
Thus, the 1st quarter for the data set is 46, 3rd quarter is 67 and the interquartile range is 21.

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As per direct variation,

Part A) Decorators fee is $198.132

Part B) Tax for the purchase is $71.10

Part C) The total amount spend by the family is $1849.232.

Direct variation:

Direct variation depicts a simple relationship between two variables . We say y varies directly with x if:

y=kx

for some constant kk , called the constant of variation or constant of proportionality. Which means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

Given,

A family used a professional decorator to furnish their new home.

The decorator selected $1,580 worth of furnishings for their home.

The payment will be made by the family for the furnishings, plus 4.5% tax on the purchases.

The decorator’s fee was 12% of the furnishings , excluding the tax.

Here we need to find the following:

Part A) Decorator's fee

Part B) Tax amount

Part C) Total cost.

We know that, the decorator’s fee was 12% of the purchases.

So, the equation is then be calculated as:

y = kx

where,

y = decorators fee

k = percentage of decorators fee for the purchases

x = amount paid

y = 12% × $1651.10

= 0.12 × $1651.10

Therefore, the decorators fee is $198.132

Decorator selected furnishings cost = $1,580.

Tax = 4.5%

Decorator’s fee = 12% of the purchases.

So, it can be calculated as,

Tax = 4.5% × 1580

Tax = 0.045 × 1580

Therefore, the tax for the purchase is $71.10

Amount paid = 1580 + 71.10 = 1651.10

Now, the total amount paid by the family is,

=> purchase amount + decorator fee

=> 1651.10 + 198.132

=> 1849.232

Therefore, the total amount spend by the family is $1849.232.

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The expression (m⁴n³)⁶will be written as (m²⁴n¹⁸) using the power property.

The power of a power property states that when we take the power of a power, we keep the base and multiply the exponents. So, (xᵃ)ᵇ= x(ᵃ×ᵇ). This shows that we write down our base and just multiply the given exponents.

Suppose, we have this problem:

(x4)3

we could multiply the exponents of the given base. This would give us:

x(⁴׳) = x¹²

In the same manner  (m⁴n³)⁶ we will multiply the exponents of the given base.

So (m⁴×⁶n³×⁶) = (m²⁴n¹⁸).

Thus we can write The following expression (m⁴n³)⁶ as  (m²⁴n¹⁸).

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Answer:

One angle measures 120°, and another angle measures (4k + 52)°. If the angles are vertical angles, determine the value of k.

Step-by-step explanation:

The number of miles that the truck drove is 550 miles.

From the information, Xin must pay the driver $20 per hour of driving and also has an expense of $2.25 per mile. This can be illustrated as:

20x + 2.25y = 1457.50 ....... i

x = number of hours

y = number of miles driven

The driver drove an average of 50 miles per hour. This will be illustrated as:

y/x = 50

y = 50x

Substitute into equation i

20x + 2.25y = 1457.50

20x + 2.25(50x) = 1457.50

20x + 112.50x = 1457.50

Collect like terms

132.50x = 1457.50

Divide

x = 1457.50 / 132.50

x = 11

y = 50x = 50 × 11 = 550 miles

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The triangle has an area of 3.37 square units

The equations are given as

y= -1/2x + 8

y = 9x

On the y-axis, the value of x is 0

i.e. x = 0

Substitute 0 for x in the equations y= -1/2x + 8 and y = 9x

So, we have

y= -1/2(0) + 8 = 8

y = 9(0)  = 0

The base of the triangle is the difference between these values

So, we have

Base = 8 - 0

Base = 0

Substitute y = 9x in y= -1/2x + 8

So, we have

9x = -1/2x + 8

This gives

9.5x = 8

Divide both sides

x = 16/19

The area of the triangle is then calculated as

Area = 0.5 * Base * x

This gives

Area = 0.5 * 8 * 16/19

Evaluate

Area = 3.37

Hence, the area of the triangle is 3.37 square units

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