Find the solution(s) of the system of equations:
y = x2 + 6x + 9
y = 2x + 6

Answer:$2.61

Step-by-step explanation:

18=$15.66

÷6    ÷6

3=$2.61

The cost of 3 bottles of juice based on the given ratio will be $2.61.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

18 bottles cost = $15.66

1 bottle cost = $15.66/18 = $0.87/ bottle

For 3 bottles = 3 × $0.87 = $2.61

Hence "The cost of 3 bottles of juice based on the given ratio will be $2.61".

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Answer:

Step-by-step explanation:

The answer is 6.

I got this by subtracting 23 by 12 (the number of numbers shown). Then I got 11. So I followed the pattern until I got six.

23-12=11

2,4,6,8,2,4,6,8,2,4,6,8,......2,4,6,8,2,4,6,8,2,4,6

The solutions are,

The radians wade sweep out is 2.875 radians.

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

When wade stops skiing, he is 0.003km above the center of the ski trail.

Given that;

Wade is traveling along a 0.8 km-radius circular ski trail. Wade moves 2.3 kilometers counterclockwise starting at the three o'clock position.

Radius (r) = 0.8km

Distance (s) = 2.3km

Here, we need to find three cases, they are;

Case(I): how many radians does wade sweep out;

The relation between radians and radius is given by,

s = rθ

2.3 = 0.8*θ

θ = 2.3/0.8

θ = 2.875

The radians wade sweep out is 2.875 radians.

Case (II): when wade stops skiing, how many km is wade to the right of the center of the ski trail;

Let, Ф = π - 2.875

      Ф = 0.266 radians

Then, x = r*cosФ

          x = 0.8*cos(0.266)

          x = 0.799

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

Case (III): when wade stops skiing, how many km is wade above the center of the ski trail;

Let, y = r*sinФ

      y = 0.8*sin(0.266)

      y = 0.003

When wade stops skiing, he is 0.003km above the center of the ski trail.

Therefore, the required solutions are;

The radians wade sweep out is 2.875 radians.

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

When wade stops skiing, he is 0.003km above the center of the ski trail.

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The probability that at least nine out of 12 cars have an acceptable emissions level is 0.333.

The branch of mathematics which deals with the analysis of random phenomena is called probability. The probability of an event is defined as the ratio of favorable events to the total number of events.

P(E) = F(E)/T(E)

Where P(E) = probability of an event which occur\

F(E) = Number of favorable events

T(E)= Total number of events

Here given that the total number of cars T(E) =12

And the number of cars that have acceptable emissions level F(E) = 4

Hence Probability that at least nine cars have an acceptable emission level

=4/12

= 1/3

= 0.333

The probability that at least nine out of 12 cars have an acceptable emissions level is 0.333.

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The identification process of direct proportion, inverse proportion and partitive proportion is show below.

Proportion is comparison of things or magnitudes in terms of size, amount.

In direct proportion, when one quantity increase or decreases, the another quantity will also increase or decrease in the same ratio.

In inverse proportion, When one quantity increases, the another quantity decreases and vise versa.

Partitive proportion is when the division of a quantity into two or more equal or unequal parts.

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The probability that a worker selected at random makes between $350 and $400 = 0.34134

What is a z score formula?

The standard score represents how far a raw score deviates from or exceeds the mean of the phenomenon being observed or measured. Positive standard scores are assigned to raw scores that are greater than the mean, while negative standard scores are assigned to raw scores that are less than the mean.

By using the z score formula:

z = (x - μ) / σ

Where,

x = raw score

μ = mean

σ = Standard deviation

We are told in the question to find the probability that a worker selected at random makes between $350 and $400

Consider, x1 = 350 and x2= 400 with the mean μ = 400 and standard deviation σ = $50.

z1 = (x1 - μ) / σ = (350-400) / 50 = -1

z2 = (x2 - μ) / σ = (400 - 400) / 50 = (0/50) = 0

From tables, P(z <= -1) = 0.15866

P(z <= 0) = 0.5

Then, the probability would give us, P(-1 ≤ z ≤ 0) =0.5 - 0.15866 = 0.34134

Hence, The probability that a worker selected at random makes between $350 and $400 = 0.34134

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Answer: 5+3*3(3)-2= 30

Step-by-step explanation: Replacing x with 2 and using PEMDAS

The product of the fractions 1/7*5/3 is 5/21.

The product of the fractions= product of the numerator/product of the denominator.

The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively.

We multiply the 1 and 5, the numerators and 7 and 3 the denominators.

Therefore the product of the fractions is 5/21.

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Answer:

5/21

Step-by-step explanation:

Given problem,

→ (1/7) × (5/3)

Let's solve the problem,

→ (1/7) × (5/3)

→ (1 × 5)/(7 × 3)

→ 5/21

Thus, the answer is 5/21.

The dimensions of algebra tile rectangles and area models can be used to represent expressions and multiplication by measuring the length and breadth of the tiles and multiplying them.

This is referred to as a quadrilateral which has four right angles and the area is calculated by multiplying the length with the breadth.

In as situation where the algebra tile rectangles is used , it is best to first measure the length and the breadth after which they are then multiplied to give the appropriate answer. For example if the length is 8cm and the breadth is 5cm then the area will be  8cm × 5cm = 40cm²

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Answer:

7

Step-by-step explanation: -13(-1) + 36 + 42(-1)

Step 1: -13(-1)= 13

Step 2: 13 + 36= 49

Step 3: 49 + 42(-1)= 49 + (-42)= 7

Solution: 7

0.7475 is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2

P( A ≥ 8.2) = P( (Z ≥ 8.2 − 8)/0.3)

= P(Z ≥0.66)

= 0.7475

normsdist(0.666666) =0.7475

The standard normal cumulative distribution function is returned. The mean of the distribution is 0 (zero), while the standard deviation is one. Instead of a table of standard normal curve areas, use this function.The concentration of hydronium (H3O+) ions in an aqueous solution is measured by pH. It is measured from 0 to 14 on a negative logarithmic scale.

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Option A is the correct choice (0.04)

The incidence rate of disease x among persons exposed to factor a is 0.04

The frequency of a particular incident over a predetermined time period is measured by the incidence rate or incidence. In the corporate world, sampling, surveys, and product testing can all be used to calculate an incidence rate.

Because 120 divided by the total number of exposed people yields the occurrence rate for disease X among those who have been exposed.

The incidence rate would be 4 per 100 people if multiplied by 100, however, this statistic is not specifically specified.

Therefore, those who were exposed to factor a had an incidence risk of disease x of 0.04

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COMPLETE QUESTION:

6,750 people who were free of disease X were enrolled in a cohort study in 1985 and followed by annual exams and interviews through 1995. Exposure to factor A was determined at study enrollment and the participants were followed until 1995 to observe new cases of disease X. Data from the study at the end of the follow-up are shown in the following table. What is the incidence rate of disease X among persons exposed to factor A? Exposure to Factor A People with Disease X People without Disease X Not Exposed 30 3,720 Exposed 120 2,880

Select one:

a. 0.04

b. 0.19

c. 0.25

d. 4.00

e. 5.17

Answer:

y = x - 3

Step-by-step explanation:

y - y1 = m( x - x1 )

y - (-2) = 1 (x - 1)

y + 2 = x - 1

y = x - 3

The region common  to both the graphs as shown is the solution set.

A system of equations is a collection of two or more equations with a same set of unknowns

Given are the following  quadratic inequalities -

x² - 6x - 7 < 0

3x² - 28x + 32 ≤ 0

We have the following quadratic inequalities -

x² - 6x - 7 < 0

3x² - 28x + 32 ≤ 0

We will plot both of them. The common region be the possible set of solutions to the given inequalities. Refer to the graph attached. The region common to both the graphs is the solution set.

Therefore, the region common  to both the graphs as shown is the solution set.

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Answer:

9/16

Step-by-step explanation:

The p-value of the distribution of population standard deviation of 33.17 texts per day is 0.9435

The test statistic's "p-value" measures how likely it is that future results will be at least as extreme as the one your sample yielded. You must understand that the null hypothesis is the underlying presumption to compute this probability.

The parameters are as follows:

The sample mean ([tex]\bar x[/tex]) = 118.4

The population standard deviation ([tex]\sigma[/tex]) = 33.17

The sample size (n) = 30

Calculate the z-score first.

[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }[/tex]

according to the entire question, x = 128

So, we have:

[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{\sqrt{30} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{5.477 } } }\\\\z = \bold{ \frac{9.6}{ 6.056} }\\\\z = 1.5852[/tex]

As determined by the z table of probability, p = 0.9435395

or p = 0.9435 (approx.)

Consequently, the distribution's p-value is 0.9435.

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By basic arithmetic, the state board of education will have $1 left .

The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.

Addition, subtraction, multiplication, and division are the four operations employed in arithmetic.

The total amount the state board has = $5647

The cost of calculator = $ 2

The total number of calculators bought = 5647/2

= 2323.5

≈ 2823

So, the cost of 2323 calculators

= 2823 × 2

= 5646

So, the money the state board of education left = $5647 - $5646

= $1

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Answer: D.

Step-by-step explanation:

Answers are attached

Answer:

Step-by-step explanation:

A coefficient is a number before the variable that shows how many groups of the variable there are. For example, 2b would be two groups of B.

The coefficients in this expression would be 4 (as in 4x) and 8 (as in 8y).

Answer:

A. 5/3

Step-by-step explanation:

The line is in a positive trend we can see it because when we read it from left to write we can see it go up. The point where we start is 5 levels down from the second point  3 units to the left.

We can model this using  rise/run

Rise = 5

Run = 3

5/3

Option b. 96,909,120 is the correct answer. The number of ways in which the new site can be chosen to locate 6 stores in 96,909,120 ways

We can find the number of ways by multiplying the number of possibilities each store can have.

Store 1, can be placed on 24 sites. Store 2 can be placed on 23 sites (since store 1 is already on site 1). Store 3 can be placed on 22 sites. Store 4 can be placed on 21 sites. Store 5 can be placed on 20 sites. Store 6 can be placed on 19 sites

Therefore the number of ways is:

C = 24 * 23 * 22 * 21 * 20 * 19

C = 9,69,09,120 possibilities

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Answer: 11.1%

Step-by-step explanation:

The formula for percent error is:

|Actual-predicted/predicted| * 100%

In the context of the problem:

Actual = 16 ft

Predicted = 18 ft

Plug these values into the equation:

|16-18/18| * 100% = percent error

11.11% = percent error
If you have any other problems about percent error, you should be able to just plug these values into the formula

The converse of the statement that says that If an item is not worth five dimes, then it is not worth two quarters is:  If an item is worth five dimes it is worth two quarters.

By swapping the hypothesis and the conclusion, a statement can be made to mean the opposite. "If two lines don't intersect, then they are parallel" is the inverse of "If two lines overlap, then they are parallel." If q, then p is the opposite of "if p, then q."

The converse of a statement may not always have the same truth value as the original. For instance, "All mammals are tigers" is the polar opposite of "All tigers are mammals." This is undoubtedly untrue.

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A system of inequality to represent the maximum amount of flooring needed is c + h ≥ 2000.

A system of inequality to represent the maximum amount of money wants to spend is 4.50c + 8.25h ≥ 10,000.

In order to solve this word problem, we would assign variables to the number of square feet of carpet and the number of square feet of hardwood for the given flooring area, and then translate the word problem into an algebraic inequality as follows:

For the maximum amount of flooring needed, we have:

c + h ≥ 2000

For the maximum amount of money, we have:

4.50c + 8.25h ≥ 10,000.

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Answer:

-------------------------

Answer:

5

Step-by-step explanation:

10+4+2+4=20

20/4=5

The mean is five.

Answer:

Mean = 5

Step-by-step explanation:

Mean = ( Sum of Data Points ) / ( Number of Data Points )

Sum of Data Points = 10 + 4 + 2 + 4 = 20

Number of Data Points = 4

Mean = 20 / 4 = 5

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By rounding each number to 1 significant figure estimate to 6235.1 x 21.5 is 120000.

The concept of significant fiqure is based on the looking for the first non zero number that is resnt in the numbers , and that will be one significant figure, and it goes like that.

Then let us round each of the given fiqures into 1 significant fiqure as instructed:

6235.1 to 1 significant figure will be 6000 , because 6 is the first significant fiqure and the value that follow 6 is less than 5, it can not been approximated

21.5 to 1 significant figure will be  20

Then (6000*20) =120000

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For x to be a solution, there must be the quantity x in the equation.

All the equations that contain x are :
+) 24 - 2x = 13
+) 4  + 5x = 18
+) 2x - 3 = 15
+) 3x + 2 = 25

We will solve for the value of x for each of the equation :

+) 24 - 2x = 13
-> 2x = 24 - 13 = 11
-> x = 11/2 = 5.5

+) 4 + 5x = 18
-> 5x = 18 - 4 = 14
-> x = 14/5 = 2.8

+) 2x - 3 = 15
-> 2x = 15 + 3 = 18
-> x = 18/2 = 9

+) 3x + 2 = 25
-> 3x = 25 - 2 = 23
-> x = 23/3.

We can see, only the equation 2x-3 = 15 has x=9 as a solution.