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Step-by-step explanation:

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a) The quadratic equation x² + 10x + 29 in vertex form is given as follows:

(x + 5)² + 4.

Meaning that the values of c and d are given as follows:

b) The coordinates of the turning point of the curve y = x² + 10x + 29 are given as follows:

(-5,4).

The quadratic function in vertex form is defined as follows:

y = x² + 10x + 29.

The first two terms of the equation can be simplified as follows:

x² + 10x = (x + 5)² - 25.

(considering the square of the addition notable product).

Hence the vertex-form definition of the quadratic function, completing the squares, is given as follows:

y = (x + 5)² + 4.

As (x + 5)² = x² + 10x + 25, hence an addition by 4 is needed to obtain 29.

This means that the coordinates of the vertex of the function, which is the turning point of the function, are of (-5,4).

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(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.

(b) The algebraic expression, 5x -2  - (5x + 2) is simplified as -4.

The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.

The given algebraic expressions are;

-5x - 2 + 5x + 2

5x -2  - (5x + 2)

The first algebraic expression is simplified as follows;

-5x - 2 + 5x + 2

collect similar terms;

(-5x + 5x) + (-2 + 2)

= 0 + 0

= 0

The second algebraic expression is simplified as follows;

5x - 2 - (5x + 2)

= 5x - 2 - 5x - 2

collect similar terms;

= (5x - 5x) + (-2 - 2)

= 0 - 4

= - 4

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The solution to the given linear inequality, r - 6 > -11, is r > -5

From the question, we are to determine the solution of the given inequality

The given inequality is

r - 6 > -11

To determine the solution of the inequality, we will solve the inequality for the unknown variable.

In the inequality, the unknown variable is r.

Solving the inequality for r

r - 6 > -11

Add 6 to both sides

r - 6 + 6 > -11 + 6

r > -5

Hence, the solution is r > -5

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Answer:

step 4

Step-by-step explanation:

she's at 6 then goes up 3 which would mean she's at step 9. then she goes does 4 so subtract 9-4=5. She would be on step 5 but she decides to go up 2 so add. 5+2=7. then she goes down 3 steps so subtract. 7-3=4. she ends up at step 4.

Answer:

\( \frac{x - 9}{2} = 5 \\ x - 9 = 5 \times 2 \\ x = 10 + 9 \\ x = 19\)

The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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Answer:

Attached file is the solutions

Step-by-step explanation:

Answer: Everyone in your population must have an equal, non-zero chance of being selected. (In other words, everyone has an equal chance of receiving a survey.) You must know, specifically, what that chance of being selected is for each person.

The given sample of the randomly selected players from the teams as described is a stratified sample. Hence, the right answer is option A.

In a stratified sample, the population is divided into groups (or strata) based on some characteristic, and a random sample is selected from each group. In this case, the population is the football players, and the groups are the varsity and junior varsity teams. The coach randomly selects one of these teams and then asks all players from that team their opinion on a new logo.

This type of sampling is used when the population is divided into subgroups that are different in some way, and the researcher wants to ensure that these subgroups are represented in the sample. In this case, the coach wants to ensure that both varsity and junior varsity players are represented in the sample, as they may have different opinions on the new logo.

It's not a simple random sample because he selected the team first and then the players. Also, it's not a voluntary response sample because the coach is selecting the players.

It's not a cluster sample because the coach is not selecting the players based on location or geographic proximity, and it's not a systematic sample because he is not selecting the players based on the order in which they appear in a list or a database.

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Answer:

27.56

Step-by-step explanation:

The standard deviation of the response time is 1.53 minutes.

To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.

Z-score = z = (x - μ) / σ

For the lower bound of 10 minutes:

z = (10 - 13) / σ

For the upper bound of 16 minutes:

z = (16 - 13) / σ

As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.

Using z-scores, we set up  equations:

(10 - 13) / σ = -1.96

(16 - 13) / σ = 1.96

Solving the first equation:

-3 / σ = -1.96

σ = -3 / -1.96

Solving the second equation:

3 / σ = 1.96

σ = 3 / 1.96

Dividing both sides by 1.96:

-3 / 1.96 = σ

1.53 = σ

Full question:

The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.

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Answer:

When the graph of the linear relationship contains the origin, the relationship is proportional. A linear equation is an equation whose solutions are ordered pairs that form a line when graphed on a coordinate plane. A relationship may be linear but not proportional and the graph does not pass through the origin.

Step-by-step explanation:

The characteristics of a graph that represents a proportional relationship:

1. Straight Line

2. Passing Through the Origin

3. Constant Ratio

4. Linear Equation

A graph is proportional when it represents a proportional relationship between two variables.

In a proportional relationship, as one variable increases or decreases, the other variable changes in a consistent and predictable manner.

The key characteristics of a graph that represents a proportional relationship:

1. Straight Line: The graph of a proportional relationship is a straight line. This means that the points on the graph fall in a straight line, indicating a constant rate of change between the two variables.

2. Passing Through the Origin: In a proportional relationship, the graph passes through the origin (0, 0). This means that when both variables are zero, they are directly proportional to each other.

3. Constant Ratio: The ratio between the values of the two variables remains constant along the entire line. This ratio is often referred to as the "constant of proportionality."

4. Linear Equation: The equation of a graph representing a proportional relationship is in the form y = kx, where "k" is the constant of proportionality.

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Answer:

28

Step-by-step explanation:

F=2.25+0.20(m-1)

7.65=2.25+0.20(m-1)

5.4=0.20(m-1)

5.4/0.20=0.20(m-1)/0.20

27=m-1

28=m

162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (d) 0.04

The margin of error is a statistic that describes how much random sampling error there is in survey results.

Given in question,

n = 400

p = 317/400

  = 0.7925

Confidence Level = 95%

                          = 0.95

Formula for margin error, E = \(z\sqrt{\frac{p(1-p)}{n} }\)

Confidence level corresponding to 95 % confidence interval, z = 1.96

Therefore,

Margin Error, E = \(1.96\sqrt{\frac{0.7925(1-0.7625)}{400} }\)

                         = 0.0397

                         ≈ 0.04

Hence, The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is 0.0397 which is closest to 0.04.

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The given function has no undefined points nor domain constraint. Thus, the domain is: \(-\infty \: < x < \infty\).

The domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined. An example, there is a restriction for the domain of fractions. The variable x in the denominator should be different of zero.

While the domain is related to the values ​​of x, the range is related to the possible values ​​of y that the function can have.

In this question, the function \(2^x\) has no undefined points nor domain constraint. Therefore, the domain is: \(-\infty \: < x < \infty\)

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An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.

This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).

Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.

Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.

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The equation of the line of best fit for this data-set is given as follows:

y = 10x + 60.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the coefficients are given as follows:

The function goes through point (0,60), hence the intercept b of the line of fit is given as follows:

b = 60.

When x increases by 2, from 0 to 2, y increases by 20, from 60 to 80, hence the slope m is obtained as follows:

m = 20/2 = 10.

Hence the line of fit is given as follows:

y = 10x + 60.

Meaning that the third option is correct.

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Answer:

y = 10x + 60.

Step-by-step explanation:

There are 2518 sets of five marbles that include either the lavender one or exactly one yellow one, but not both.

To solve this problem, we need to find the number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both colors. Here's one way to approach the problem:

Number of sets of five marbles that include the lavender one: There is only one lavender marble, so we can choose any 4 other marbles to go with it.

There are a total of 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 7 x 6 x 5 x 4 = 840 possible sets of five marbles that include the lavender one.

Number of sets of five marbles that include exactly one yellow one: There are two yellow marbles,

So there are 2 possible choices for the yellow marble. For each choice, we can choose any 4 other marbles to go with it.

As before, there are 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.

This gives us a total of 2 x (7 x 6 x 5 x 4) = 1680 possible sets of five marbles that include exactly one yellow one.

Number of sets of five marbles that include both the lavender one and exactly one yellow one:

We need to subtract these sets from the total number of sets that include either the lavender one or exactly one yellow one.

We have already found that there are 840 sets of five marbles that include the lavender one, and 1680 that include exactly one yellow one.

To find the number of sets that include both, we can choose any one yellow marble and the lavender one.

There are 2 choices for the yellow marble and 1 choice for the lavender one,

So there are 2 x 1 = 2 possible sets of five marbles that include both the lavender one and exactly one yellow one.

Number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both:

Finally, we need to subtract the number of sets that include both the lavender one and exactly one yellow one from the total number of sets that include either the lavender one or exactly one yellow one.

The total number of sets that include either the lavender one or exactly one yellow one is 840 + 1680 = 2520. The number of sets that include both is 2,

So the number of sets that include either the lavender one or exactly one yellow one, but not both, is 2520 - 2 = 2518.

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We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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Answer:

$25-$9.9

Step-by-step explanation:

45/100

0.45*$25

$9.9

$25-$9.9

it cost 14.1

Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

Answer:

\(\huge \boxed{{x\geq -3, \ x \neq 2}}\)

Step-by-step explanation:

The function is given,

\(\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}\)

The domain of a function are all possible values of x.

There are restrictions for the value of x.

The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.

\(x+8\neq 0\)

Subtract 8 from both parts.

\(x\neq -8\)

\(x-2\neq 0\)

Add 2 on both parts.

\(x\neq 2\)

The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.

\(x+3\geq 0\)

Subtract 3 from both parts.

\(x\geq -3\)

The domain of the function is \(x\geq -3\), \(x\neq 2\).

The domain of the given function will be x ≥ -3 and x ≠ 2.

The entire range of independent input variables that can exist is referred to as a function's domain or,

The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.

As per the data given in the question,

The given expression of function is,

f(x) = \(\sqrt{\frac{x+3}{(x-8)(x-2)} }\)

The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.

x + 8 ≠ 0

x ≠ -8

And, x - 2 ≠ 0

x ≠ 2

Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.

So,

x + 3 ≥ 0

x ≥ -3

So, the domain of the function will be x ≥ -3 and x ≠ 2.

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Answer:

x=125

Step-by-step explanation:

Answer:

37.50 UNITS SQUARE.

Step-by-step explanation:

add 6 to 9 you get 15

multiply 15 by 5 you get 75

divide 75 by 2

37.5

I hope it helps bye

Answer: We need to translate the phrase "b times 5" Into algebraic expression, the algebraic expression is as follows:

Answer:

1.length = 15, width = 12, height = 13

2. 13 × 12 × 15 = 2340

Step-by-step explanation:

3 ÷ 1/4 = 12

3 3/4 = 15/4

15/4 ÷ 1/4 = 15

3 1/4 ÷ 1/4 = 13

length = 15

width = 12

height = 13

13 × 12 × 15 = 2340