Solve the system of linear equations by substitution.

6x-9=y

y=-3x

11/21 as a decimal rounded to the nearest tenth is 0.5. Below, you will learn how to solve the problem.

To convert the fraction 11/21 to a decimal rounded to the nearest tenth, we can follow these steps:

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The inequalities represented on the graph is x ≥ -2.

In mathematics, an inequality is a mathematical expression where neither side is equal. Inequality in mathematics is defined as a comparison between two expressions or two numbers that is not equal. In mathematics, there are several varieties of inequality, including polynomial inequality, rational inequality, and absolute value inequality.

Given that,

Number line showing range from negative five to five. The left end point is a closed dot at negative two, with a ray pointing right past five.

From the above we observe that point on negative 2 is a closed dot hence the inequality would be ≥ or ≤.

Now, the ray point past five, that is it moves in positive direction.

Hence, the inequalities represented on the graph is x ≥ -2.

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The results of the first three trials are:

Trial 1: 8 girls, 12 boys

Trial 2: 13 girls, 7 boys

Trial 3: 11 girls, 9 boys

What is permutation and combination ?

Permutation and combination are two related concepts in mathematics that deal with counting and arranging objects.

Permutation refers to the number of ways in which a set of objects can be arranged or ordered. In other words, it involves selecting objects from a set and arranging them in a specific order. The formula for finding the number of permutations of n objects taken r at a time is given by:

nPr = n! / (n-r)!

According to given condition:

To simulate the number of male and female births using a random digit table, the nurse has assigned the digits 0-4 to represent girls and 5-9 to represent boys. She selects samples of 20 and records the digits in order.

For the first trial, the digits are:

1 7 9 3 9 6 7 7 6 4 0 7 1 3 4 9 9 0 4 7

Interpreting these digits using the nurse's coding scheme, we see that there are:

8 girls (represented by the digits 0-4)

12 boys (represented by the digits 5-9)

For the second trial, the digits are:

6 2 4 5 4 8 1 0 6 9 0 7 8 7 9 8 5 4 2 8

Interpreting these digits using the nurse's coding scheme, we see that there are:

13 girls

7 boys

For the third trial, the digits are:

5 9 3 9 8 4 1 8 2 2 4 6 4 8 0 3 3

Interpreting these digits using the nurse's coding scheme, we see that there are:

11 girls

9 boys

Therefore, the results of the first three trials are:

Trial 1: 8 girls, 12 boys

Trial 2: 13 girls, 7 boys

Trial 3: 11 girls, 9 boys

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Using proportions, we determined 24 out of every 36 households have a guest room.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, six out of every 9 households have a guest room.

So, the ratio is 6:9

Margaret asked x households in her neighborhood if they have a guest room, and 24 said yes

So, the ratio is 24:x

Now, the proportion is 6:9::24:x

6x=9×24

x=36

Hence, 24 out of every 36 households have a guest room.

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Answer:

$1.24

Step-by-step explanation:

use a proportion.

$3.10/5 = x/2

5x = 2 × $3.10

x = $1.24

Answer:

$1.24

Step-by-step explanation:

$3.10 for 5 bags

I bag = 310/5= 62

Move the decimal point back two times which is 0.62

2 bags cost 0.62*2= 1.24

= $1.24

2.16% probability that the man would have done at least this well if he had no ESP.

As we know that for each coin toss, there are only two possible outcomes. Either he predicts the correct outcome, or he does not. Therefore, the tosses are independent. So, we can use the binomial probability distribution:

Binomial probability distribution says that, the binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X=x) = Cₙ, ₓ.pˣ.(1-p) ⁿ⁻ˣ

here, Cₙ, ₓ is the number of different combinations of the x objects from a set of n elements, which is given by the following formula:

Cₙ, ₓ = n/x(n-x)

here, p is the probability of X happening, therefore,

fair coin: Equally as likely to be heads or tails, so p = 0.5

number of times coin is flipped = 22

n = 22

now for the probability that he would have done at least this well if he had no ESP:

P(X>16) = P(X=16) + P(X=17) + P(X=18) + P(X=19) + P(X=20) + P(X=21) + P(X=22)

In which;

P(X = 16) = 0.0143; P(X = 17) = 0.0053; P(X = 18) = 0.0016; P(X = 19) = 0.0004; P(X = 20) = 0.0001

for the other values we know that they are close to 0, hence,

P(X>16) = P(X=16) + P(X=17) + P(X=18) + P(X=19) + P(X=20) + P(X=21) + P(X=22) = 0.0216

So we know that 2.16% probability that he would have done at least this well if he had no ESP

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Answer:a

Step-by-step explanation:

Step-by-step explanation:

6 notebooks = $d

1 notebook = $?

So

1 notebook price = $d ÷ 6

Answer:

Step-by-step explanation:

n represents the number of notebooks

d represents the cost of a notebook

n = d            one notebook = d dollars

9n = 9d        multiply both sides by 9

In the triangle BCD the value of ∠BDC is 105°.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

In ΔABC and ΔBCD it is given that -

∠A ≅ ∠B

∠ADC ≅ ∠BCD

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

So, by the theorem stated above -

∠ACD ≅ ∠BDC

In ΔACD he sum of angles of a triangle is 180°.

The equation will be -

∠ACD + ∠ADC + ∠A = 180°

Substitute the values in the equation -

∠ACD + 30° + 45° = 180°

∠ACD + 75° = 180°

∠ACD = 180° - 75°

∠ACD = 105°

Now, since ∠ACD ≅ ∠BDC.

So, ∠BDC = 105°.

Therefore, the measure of ∠BDC is 105°.

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Radians are multiplied by 180° radians to convert to degrees.

A unit of measurement for angles that is about 57.3°, or the angle covered in the center of a circle by an arc that has the same length as the radius.

Conversion factor between radians and degrees

One radian, or degree, equals 0.01745329252:

1° = π/180°

0.005555556π = 0.01745329252 rad

There are 57.295779513 radians in a degree.

1 rad = 180°/π \s= 57.295779513°

The angle in degrees is equal to the angle in radians times 180 degrees divided by the constant pi: degrees = radians 180° /

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The equation √(x - 1) - 5 = x - 8 has two solutions 2 and 5. The valid solution is 5.

The set of values that can be satisfies the given condition in the equation is known as the solution.  We can solve the equation by adding or subtracting the same integer from both sides. Here adding or subtracting doesn't change the value of the equation.

Here we have

√(x - 1) - 5 = x - 8  

Solve the above equation to get the solutions

√(x - 1) - 5 = x - 8    

Add 5 on both sides

√(x - 1) - 5 + 5 = x - 8 + 5

√(x - 1)  = x - 3  

Do squaring on both sides

[√(x - 1) ]² = (x - 3)²    

[ x - 1 ] = (x² + 9 - 6x)    

x² + 9 - 6x - x + 1 = 0

x² - 7x + 10 = 0  

Now factorize the above equation

x² - 5x - 2x + 10 = 0      

x(x - 5) - 2(x - 5) = 0

(x - 5) (x - 2) = 0

(x - 5) = 0     and     (x - 2) = 0

x = 5                       x = 2      

at x = 2 => √(2 - 1) - 5 = 2 - 8    

=> √1 - 5 = 2 - 8    

=>   - 4 = -6 [ which is not true ]

at x = 5 => √(5 - 1) - 5 = 5 - 8      

=> √(4 - 1) - 5 = - 3  

=> 2 - 5 = -3  [ which is true ]

Therefore,

The equation √(x - 1) - 5 = x - 8 has two solutions 2 and 5. The valid solution is 5.

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Answer:

Step-by-step explanation:

The sum of exterior angles of a polygon is 360

Each exterior angle = 360/n

where n is the number of sides

360/12 = 30

Answer is D

Answer:

Plug in the variable (x) in the equation.

Step-by-step explanation:

once you plug it in, multiplied by two, and subtract by 3, and it should equal your y input

Answer:

[tex]\frac{19}{24}[/tex]

Step-by-step explanation:

You need a common denominator so the pieces are equal sizes.  The common denominators is 24

[tex]\frac{4}{6}[/tex] x [tex]\frac{4}{4}[/tex] = [tex]\frac{16}{24}[/tex]

[tex]\frac{1}{8}[/tex] x [tex]\frac{3}{3}[/tex] = [tex]\frac{3}{24}[/tex]

[tex]\frac{16}{24}[/tex] + [tex]\frac{3}{24}[/tex] = [tex]\frac{19}{24}[/tex]

Answer:

[tex]\frac{2}{4}[/tex] or [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

When each time a coin is flipped, there are two possible outcomes.

The chance for either heads or tails being chosen is one half.

Thus, the number of times the coin can be flipped and land on heads or tails is [tex]\frac{1}{2}[/tex].

Hope it helped!

The probability that a randomly selected first-year teacher makes less than $20,000 a year is approximately 0.0071.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

To solve this problem, we can use the normal distribution and the standard normal distribution table (also known as the z-table).

Let X be the salary of a first-year teacher. We are given that X is approximately normally distributed with a mean (average) of mu = $27,989 and a standard deviation of sigma = $3250. We want to find the probability that a randomly selected first-year teacher makes certain salaries.

A. Between $20,000 and $30,000 a year

To find the probability that a first-year teacher makes between $20,000 and $30,000 a year, we need to standardize the interval using the z-score formula:

z1 = (20000 - mu) / sigma = (20000 - 27989) / 3250 = -2.45

z2 = (30000 - mu) / sigma = (30000 - 27989) / 3250 = 0.63

Using a standard normal distribution table or calculator, we can find that the probability of a random variable being between z1 and z2 is approximately 0.8461.

Therefore, the probability that a randomly selected first-year teacher makes between $20,000 and $30,000 a year is approximately 0.8461.

B. Less than $20,000 a year

To find the probability that a first-year teacher makes less than $20,000 a year, we need to standardize this value using the z-score formula:

z = (20000 - mu) / sigma = (20000 - 27989) / 3250 = -2.45

Using a standard normal distribution table or calculator, we can find that the probability of a random variable being less than z is approximately 0.0071.

Therefore, the probability that a randomly selected first-year teacher makes less than $20,000 a year is approximately 0.0071.

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Answer:

-3, 1, 5, 9

Step-by-step explanation:

Read the y-coordinate of each point.

The median age of the runners is 23.5.

By adding up all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined. The median is the middle when a data set is sorted from least to greatest.

We must first arrange the ages from youngest to oldest in order to determine the median:

14, 15, 16, 19, 19, 23, 24, 27, 30, 31, 31, 33

The median will be the average of the sixth and seventh values in this sorted list because there are 12 runners:

(23 + 24) / 2 = 23.5 is the median.

Hence, 23.5 is the runners' median age.

The median, in terms of meaning, is the data set's middle value. In this instance, the age is the exact midpoint between the ages of the 12 racers. It is a central tendency index that shows how typical or representative the data are.

In this situation, the median age of 23.5 can be interpreted as the typical age of the marathon runners. Half of the runners were over 23.5 years old, and half were under that age. Although the middle figure is closer to the lower end of the age spectrum than the higher end, it can also help us estimate the runners' age range. The disparity between the runners' lowest and highest ages is not, however, directly shown.

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We utilize the differentiation method to obtain the derivative of a function. This entails calculating the limit of the ratio of the change in output (y value) to the change in input (x value). The formula then yields the function's derivative. f'(x) = [tex]\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}[/tex].

Determining the derivative of a function is a simple process. Initially, you must establish the sort of function you are dealing with.

Once the kind of function has been decided, the variables of the function must be identified.

The power rule is then used to determine the derivative of each of the terms.

Lastly, you must combine all of the terms to obtain the overall derivative.

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The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.
The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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Sure! A table of values for f(x) = log base 8 of x is shown below:

x) f(x)

1) 0

2) 1/3

3) 0.54

4) 0.67

5)0.79

6)0.89

7) 0.97

8) 1

9) 1.10

10) 1.18

A logarithmic function is a type of mathematical function that involves the use of logarithms. Logarithms are a way of expressing numbers in terms of exponents, and logarithmic functions are functions that involve the logarithm of one or more variables.

The general form of a logarithmic function is:

f(x) = log_b(x)

where b is the base of the logarithm, and x is the argument of the logarithm.

Logarithmic functions have several important properties. One of the main properties is that they can be used to convert between exponential and logarithmic forms of equations. For example, the equation[tex]2^3[/tex] = 8 can be written in a logarithmic form as log_2(8) = 3.

Logarithmic functions are also used in many applications in science, engineering, and finance. In science, logarithmic functions are used to describe the behavior of phenomena that exhibit exponential growth or decay, such as radioactive decay or population growth. In finance, logarithmic functions are used to calculate compound interest and to model the growth of investments over time.

The graph of a logarithmic function is a curve that approaches but never touches the x-axis as the x approaches zero. The shape of the curve depends on the base of the logarithm, and it becomes steeper as the base gets larger. The inverse function of a logarithmic function is an exponential function.

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The mass of 1 whole pizza will be 384 g.

What is Proportion ?

A part, piece, or number that is measured in comparison to a total is referred to as a proportion in general. When two ratios are equal, according to the definition of proportion, they are in proportion. It is a formula or claim that shows that two ratios or fractions are equivalent.

He has cut 1st pizza into 24 slices and other pizza into 8 slices.

Let the mass of small slice to be "x" g

So, the mass of large slice will be " 32+x " g

Now, Ben has two identical pizzas, it means the mass of both pizzas will be same.

So, mass of 1st pizza = mass of other pizza

                        24 x   =  8 ( 32+x )

                        24x = 256 + 8x

                        16x = 256

                         x = 16

Hence, the mass of 1 whole pizza = 24 × 16 = 384 g.

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32 ounces make up a quart. This is a common unit of measurement in the US and other nations that follow the imperial system. Two pints, four cups, or 0.946 liters make up a quart.

The Latin word quartus, which means "fourth," is where the word "quart" originates. This is due to the fact that a quart is 128 ounces or one-fourth of a gallon. A quart is a standard unit of measurement for liquid volumes in the dairy sector, as well as in cooking and baking.

In conclusion, the unit of measurement known as a quart is equivalent to 32 ounces or one-fourth of a gallon. It is frequently employed in dairy production, baking, and cooking. When measuring and preparing components, it's crucial to comprehend how to convert between quarts and other measurement units.

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In general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect the mean (average) of the data set.

This is because the mean is calculated by summing all the values in the data set and dividing by the total number of values. As the sample size increases, the influence of any individual value on the mean becomes smaller. An extremely large outlier may have a significant impact on the sum of the data set, but if the sample size is large enough, the impact on the mean will be relatively small.

However, adding an extremely large outlier to a data set can substantially affect other measures of central tendency and dispersion, such as the median and standard deviation. These measures are based on the order and spread of the data, rather than the sum of the data, and may be more sensitive to extreme values.

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Answer:

Infinite (∞)

Step-by-step explanation:

A multiple in math are the numbers you get when you multiply a certain number by another number or integer.

Multiples of 10 are numbers that can be divided exactly by 10. The multiples of a number are infinite.

Jill can water 52 plants.

A measurement of volume or capacity in the US Customary System that is equivalent to 14 gallons or 32 ounces and is used for liquids (0.95 liter).

We must divide the pail's overall capacity by the quantity of water required by each plant to determine how many plants Jill can water.

Let's first translate 6 1/2 gallons into a mixed number:

6 1/2 = 13/2

Then, we can divide the pail's total capacity by the quantity of water that each plant requires:

(13/2) / (1/8) = (13/2) * (8/1) = 104/2 = 52

Jill is then able to water 52 plants.

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If the cost of 3/4 tons of wood chips is $21 then the cost per ton of wood chips is $28.

To find the cost per ton of wood chips, we need to first determine the total cost of 1 ton of wood chips. We know that the cost of 3/4 tons of wood chips is $21, so we can set up a proportion:

3/4 tons / 21 = 1 ton / x

where x is the unknown cost per ton.

To solve for x, we can cross-multiply and simplify:

3/4 tons × x = 21 × 1 ton

3/4 x = 21

x = 21 / (3/4)

x = 28

Therefore, the cost per ton of wood chips is $28.

Finding the cost per ton is a common problem encountered in many industries, particularly those that deal with bulk materials such as wood chips, sand, gravel, or other aggregates. To calculate the cost per ton, it is important to know the total cost of the material and the total weight (or volume) of the material. It's important to note that this method works for any bulk material, as long as the weight (or volume) and cost are known. This information can be used to make informed decisions about purchasing and budgeting for materials, as well as comparing costs across different suppliers.

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Answer:

The correct answer is A. One unique triangle. This is because the sum of the angles in a triangle must equal 180 degrees, so with the given angles, only one unique triangle can be created.

Answer: A!

Step-by-step explanation:

I did it on a Module Test and it was correct!