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Answer:

the value of b is 12.

Step-by-step explanation:

To find the value of b, we can use the vertex form of a quadratic function, which is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Since we know the vertex of this parabola from the table, we can use that information to write the equation in vertex form: f(x) = a(x + 6)^2 + 8

Expanding this, we get f(x) = a(x^2 + 12x + 36) + 8

Comparing this with the standard form, we see that a = 1, b = 12, and c = 8.

Therefore, the value of b is 12.

The number of possible outcomes when you roll the die would be 6

A die is known to have only 6 faces. The 6 faces are numbered from number 1 to number 6

Such that the sample space that we would have would be given as

SS = {1, 2, 3, 4, 5, 6}

Hence the number of outcomes that we would be able to have from one die would be given as 6

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The kind of sample described in the given information is a stratified random sample.

What is stratified random sample ?

A stratified random sample is a type of probability sampling method used to obtain a representative sample of a population by dividing the population into smaller, more homogeneous groups called strata, and then selecting a random sample from each stratum.

This method is used when the population has certain characteristics or subgroups that are of interest to the researcher, and the goal is to ensure that the sample accurately represents each subgroup in proportion to its size in the population.

The process of selecting a stratified random sample involves dividing the population into strata based on some relevant characteristic, such as age, gender, education level, income, or geographic location. Then, a random sample is selected from each stratum, using a simple random sampling method. The sample size from each stratum is proportional to the size of that stratum in the population.

The advantage of a stratified random sample is that it can provide a more accurate representation of the population than other types of sampling methods, as it ensures that each subgroup is adequately represented in the sample.

According to given information :

The population of interest is people age 60 or older from the three surrounding counties. To obtain a representative sample of the population, the director of the hospital pharmacy has divided the population into three strata (i.e., the three surrounding counties) and selected a random sample of 100 people age 60 or older from each stratum. This ensures that the sample includes a proportionate number of participants from each county, which should help to reduce the potential for sampling bias that might result from selecting participants from only one county.

Therefore, this is an example of a stratified random sample.

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The maximum number of students the school can add if it wants to maintain a ratio of student to teachers 20 : 1 is 210.

Ratio defines the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of student to teachers now = 150 : 18

Ratio of student to teachers to maintain = 20 : 1

For 1 teacher , number of students needed = 20

For 18 teachers, number of students needed = 20 × 18 = 360

Present number of students for 18 teachers = 150

Maximum number of students who can be added = 360 - 150 = 210

Hence school can add a maximum of 210 students in order to maintain a ratio of student to teachers 20:1.

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1) All boys: Probability = 1/16 , 2) All girls: Probability = 1/16, 3) Exactly 3 boys: Probability = 5/16, 4) At least 1 boy: Probability = 15/16, 5) At most 3 girls: Probability = 15/16.

1) All boys: There are 16 possible combinations of 4 children, with each gender combination having an equal probability of 1/16. Therefore, the probability of all boys is 1/16.

2) All girls: Similarly, the probability of all girls is also 1/16.

3) Exactly 3 boys: To find the probability of exactly 3 boys, we need to consider all the cases with 3 boys and 1 girl. There are 4 possible combinations of 3 boys and 1 girl, so the probability of exactly 3 boys is 4/16, or 5/16.

4) At least 1 boy: To find the probability of at least 1 boy, we need to consider all the cases with 1, 2, 3, or 4 boys. There are 15 possible combinations with at least 1 boy (1 boy, 2 boys, 3 boys, and 4 boys), so the probability of at least 1 boy is 15/16.

5) At most 3 girls: To find the probability of at most 3 girls, we need to consider all the cases with 0, 1, 2, or 3 girls. There are 15 possible combinations with at most 3 girls (0 girls, 1 girl, 2 girls, and 3 girls), so the probability of at most 3 girls is 15/16.

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To choose that a matrix is neither a diagonal matrix and are not scalar multiples of each other. The matrices will be as:

A = [ 2 1 ; 1 2 ]

B = [ -2 1 ; 1 2 ]

The matrices shown above can be used to find invertible matrices. The sum of A and B is [0 2; 2 4], which has a non-zero determinant and is therefore invertible. This choice of A and B satisfies the given conditions because they have different eigenvalues, ensuring they are not scalar multiples of each other, and are also not diagonal matrices.

The key idea behind this choice was to use matrices with the same trace and determinant, which guarantees that their sum will have the same determinant as well. This method allows us to construct examples of invertible matrices that satisfy the given conditions.

The complete question is provided in the image below.

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Answer:

The answer to the expression, (x + 6)^2 is [tex]x^2+12x+36[/tex].

Step-by-step explanation:

We can solve this problem by breaking (x + 6)^2 into (x + 6) (x + 6).  Now, we can use FOIL to figure out the expression that is equivalent to the problem.

(x + 6) (x + 6)

First, we multiply the Xs together.

[tex]x*x=x^2[/tex]

Next, is the Outer values.

[tex]x*6=6x[/tex]

Third, we multiply the Inner values.

[tex]6*x=6x[/tex]

Finally, we can multiply the Last values.

[tex]6*6=36[/tex]

Now, we can put it all together.

[tex]x^2+6x+6x+36[/tex]

We still have one more step left.  Add like terms.

[tex]x^2+12x+36[/tex]

The answer is [tex]x^2+12x+36[/tex].

The solution is, the nth term of the arithmetic sequence 4,7,10,13 is 1 + 3n.

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.

The nth term of AP : a_n = a + (n – 1) × d

here, we have,

the arithmetic sequence 4,7,10,13

so. we get,

1st term = 4 = a

common difference = 3 = d

i.e.  the nth term of the arithmetic sequence is, a_n = 4+(n-1)3

                                                                                      =1+3n

Hence, The solution is, the nth term of the arithmetic sequence 4,7,10,13 is 1 + 3n.

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[tex]D(x)=\frac{f(x)}{g(x)}[/tex]

[tex]D'(x)=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }[/tex]

Quotient rule in calculus is method finding the derivative of the differentiable functions which are in the division form

There are different methods to prove the quotient rule formula, given as,

Here, we are using implicit differentiation method to solve this quotient rule,

Let us take a differentiable function ,

[tex]D(x)=\frac{f(x)}{g(x)}[/tex]--------(1)

So, [tex]f(x)={D(x)}*{g(x)}[/tex]

Using the product rule we get,

[tex]f'(x)= D'(x).g(x)+g'(x).D(x)[/tex] solving for [tex]D'(x)[/tex] we get,

[tex]\frac{f'(x)-g'(x).D(x)}{g(x)} = D'(x)[/tex]------(2)

substitute for D(x) sub (1) in (2)

[tex]D'(x) =\frac{f'(x)-g'(x).\frac{f(x)}{g(x)} }{g(x)}[/tex]

⇒[tex]D'(x) =\frac{f'(x)g(x)-g'(x){f(x)} }{(g(x))^{2} }[/tex]

Hence,[tex]D'(x)=\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^{2} }[/tex] proved.

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Answer:

55 L of water

Step-by-step explanation:

11-L of 60% acid contains 0.6 × 11 L = 6.6 L acid

Let x = amount of pure water.

Let y = total amount produced of 90% water solution.

A 90% water solution is a 10% acid solution.

Amounts of solutions:

x + 11 = y

Amounts of acid:

6.6 = 0.1y

y = 66

x + 11 = 66

x = 55

Answer: 55 L of water

55 L water has 0 acid.

11 L 60% acid solution has 6.6 L acid.

66 L of 10% acid solution has 6.6 L acid

Answer:

5

Step-by-step explanation:

6/1.2=5

The model would be 2 inches wide.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

Given:

A model is being built of a car.

The car is 12 feet long and 6 feet wide.

The length of the model is 4 inches.

The scale factor x is,

= 4/12

= 1/3

The width of the model is,

= 6 x 1/3

= 2 inches.

Therefore, the width is 2 inches.

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Equating the mathematical expressions, we can determine that the siblings need to sell 12 bags of cookies for them to raise the same amount of money.

Mathematical expressions are the combination of variables, constants, numbers, and values using mathematical operands like addition and subtraction.

Mathematical expressions are also described as algebraic expressions.

The initial amount that you have = $24

Your selling price per bag of cookies, c, = $3

The total amount you will make is given by Expression 1: 24 + 3c

Your sister's selling price per bag of cookies, c, = $5

The total amount your sister will generate is given by Expression 2: 5c

To determine the number of bags of cookies you must sell to raise the same amount of money between the two siblings, we equate the two expressions as follows:

24 + 3c = 5c

24 = 2c

12 = c

Check:

5c = 60 (5 x 12)

24 _ 3c = 60 (24 + 36)

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Answer:Angle 6 and Angle 5, Angle 3 and Angle 2

100% correct don't worry ;)

Step-by-step explanation:

Answer:

23:15 as a decimal and 23 3/20

Step-by-step explanation:

Just divide by 100 to get decimal. For the fraction divide by 100 and simplify

The value of x is x= π/8

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

2tan x/1-tan² x= 1

We know that tan π/4= 1

So, 2tan x/1-tan² x= tan π/4

Also, we know that tan 2x=  2tan x/1-tan² x

Again, 2tan x/1-tan² x= tan π/4

tan 2x= tan π/4

Now comparing we get

2x= π/4

x= π/8

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The simplified expression of p^8/p^7 is given as follows:

p.

The expression for this problem is defined as follows:

p^8/p^7.

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence the subtraction of the exponents is given as follows:

8 - 7.

Meaning that the simplified expression of p^8/p^7 is given as follows:

p.

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The Equation of line perpendicular to line y = x + 1 and passes through (8,-3) is y= -x+ 5.

A line's  b is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the  change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Equation: y= x+ 11

Now, the slope of perpendicular have the slope equal to negative reciprocal so that the product of slope of perpendicular line is -1.

Then, the slope of perpendicular line is, m= -1.

As, line passes through (8, -3) then the slope intercept form

y= mx+ b

-3 = (-1)(8)+ b

-3 = -8 +b

b= 5

Thus, the Equation of line is y= -x+ 5.

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The length of the line QR is 3 units. Options A

The properties of a pentagon is expressed as;

From the image shown, we have that;

The point from Q to R are (-8, -5)

To determine the distance, we have that;

-8-(-5)

-8 + 5

Add the values

-3

Hence, the number  is 3

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The value of y is 45.

Those triangles look the same but are different in size.

And in similar triangles,

the corresponding sides are in proportion to each other and the corresponding angles are equal to each other.

Given:

The shape of the triangle is given in the image.

Assuming the shape is ABC.

And the segment that is parallel to the base side of the triangle is DE.

BC II DE.

So, the triangle ΔADE is similar to ΔABC.

So, the corresponding sides have a constant proportion.

So, y/15 = (20 + 10)/10

y = 15 x 3

y = 45.

Therefore, y = 45.

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(a) A distance r from the cylinder axis is pr/2∈₀ and (b) expression for E when r > R is πR²lρ/2πϵ₀

(a) Consider a Gaussian surface in the form of a cylinder with radius r and length A, coaxial with the charged cylinder. An “end view” of the Gaussian surface is shown as a dashed circle. The charge enclosed by it is

q = ρV = πr²lp

V = volume of cylinder

If ρ is positive, the electric field lines are radially outward, normal to the Gaussian surface, and distributed uniformly along with it. Thus, the total flux through the Gaussian cylinder is  Φ = E(2πrl). Now, Gauss’ law leads to :

2π∈₀rlE = πr²lp

E = pr/2∈₀

(b) ) Next, we consider a cylindrical Gaussian surface of radius r > R. If the external field [tex]E_{ext}[/tex] then the flux is  Φ=2πϵ₀[tex]E_{ext}[/tex]

​ The charge enclosed is the total charge in a section of the charged cylinder with length A. That is,  q=πR²lρ. In this case, Gauss’ law yields :

2πϵ₀[tex]E_{ext}[/tex] = πR²lρ

[tex]E_{ext}[/tex] = πR²lρ/2πϵ₀

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The process that will create a congruent figure is a translation of four units up, followed by a rotation (option B).

A figure is said to be congruent with another if they both have the same shape and the dimensions are the same. This means the figures are almost identical, although it is allowed that they are a reflection or that they are placed in the opposite direction.

Based on this, to create a congruent figure you need to translate the original figure and rotate it but not change its size (option B).

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The range of the graph is,

⇒ Range = { y | - 1 < y < 3 }

The domain of the graph is,

⇒ Domain = { x | - 4 < x < 2 }

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph is shown in figure.

Now, We know that;

The range of the graph is the value of y where the function of graph is defined.

Hence, The range of the graph is,

⇒ Range = { y | - 1 < y < 3 }

And, The domain of the function is defined the value of y where the function of graph is defined.

Hence, The domain of graph is,

⇒ Domain = { x | - 4 < x < 2 }

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The square of the monomial 0.16x^2y^2 can be expressed as:

(0.16x^2y^2)^2 = 0.16^2 * x^2 * y^2 * x^2 * y^2 = 0.0256x^4y^4

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The mean (μ) and standard deviation (σ) represent the parameters of a normal distribution, so in this case, the parameters of the distribution are: μ = 80 transactions and σ = 10 transactions

A normal distribution, also known as a Gaussian distribution, is a continuous probability distribution that has a bell-shaped curve. This type of distribution is often used to model real-world phenomena that are expected to be distributed in a symmetrical fashion around a central value.

The central value of a normal distribution is the mean (μ), which represents the average of all the observations in the distribution. The spread or dispersion of the distribution is measured by the standard deviation (σ), which indicates how much the observations deviate from the mean.

In the given problem, the distribution of the number of transactions per day at an ATM is assumed to be normal with a mean of 80 transactions and a standard deviation of 10 transactions.

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Using the sketch, the possible range of values of x for which 2x² + 3x - 2≤0 is [-2, 0.5].

The domain of a function is a possible set of values of the independent variable. Based on the domain of a function, the codomain and range are determined.

Take the inequality as 2x²+3x-2≤0.

Solve the inequality.

2x²+3x-2≤0

(2x-1)(x+2)≤0

→ -2≤x≤0.5

The inequality is sketched in the graph and the area is also shaded for which 2x²+3x-2≤0. The range values of x mean the set of all points in the inequality -2≤x≤0.5, that is, [-2, 0.5].

Therefore, the obtained answer is [-2, 0.5].

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The missing statements and reasons in the two column proof are;

1. AOC and BOD.

2. All radii of a circle are congruent

3. SAS congruency theorem

4. CPCTC

A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons that we know those statements are true.

The two column proof of the angles is;

Statement 1: Central angles ∠AOC and ∠BOD are congruent

Reason 1: Given

Statement 2: The segments AO, CO, BO, and DO are congruent

Reason 2: All radii of a circle are congruent

Statement 3: Triangle AOC is congruent to triangle BOD

Reason 3: SAS congruency theorem

Statement 4: Chord AC is congruent to chord BD

Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

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